Is Anthony Davis the kind of player coaches dream about?

Monty Williams didn’t take much time to ponder the question or equivocate in his answer.

“There’s no question about it,” he said. “As a coach, you pray and you pray and you pray that a player like this will come along. I’m very thankful.”

That may have been the first time Williams has said that publicly about his third-year power forward. But it was far from the first time Davis has heard it from his coach.

“When I first came here, he would always tell me that I had something inside me that doesn’t come around often,” Davis said. “And it means a lot, coming from a coach who’s been around some of the league’s best coaches, been on great coaching staffs, played with great players and seen a lot of things. When he says that, it makes me want to work even harder.”

The rest of the basketball world should consider itself notified: Going into his third season, Davis is the game’s next emerging superstar.

“Anthony Davis is not just on the rise,” said Oklahoma City Thunder coach Scott Brooks, who has his own MVP in Kevin Durant. “He’s there already.”

It’s precisely that sublime combination of talent and desire that made Davis the first pick in the 2012 draft — Kentucky teammate and fellow freshman Michael Kidd-Gilchrist was chosen second — after the then-Hornets had beaten the lottery odds to get the No. 1 spot.

That faith has been rewarded as Davis has progressed from All-Rookie to All-Star last season (albeit as an injury substitute for Kobe Bryant) to one of the league’s elite players.

Playing a leading role on the gold-medal winning U.S. team in the World Cup this summer, after being basically a teenage tagalong on the 2012 Olympic team, has added to his burgeoning reputation.

Many are calling Davis the league’s best player under the age of 25 — and he’s just 21. His player efficiency rating from last season was fourth in the league and the highest number for anyone his age in the 20-year history of the statistic, which measures a player performance in 10 areas. ESPN on Monday ranked Davis the third-best player in the league.

He passes the eyeball test, too.

“Anthony Davis has become a star,” ESPN analyst Avery Johnson said. “Here’s a guy who really doesn’t have any major weaknesses and has such major strengths at such a young age.

“To me, he has the same DNA as Dirk Nowitzki (whom Johnson played with and coached with the Dallas Mavericks). He’s just going to keep getting better and better.”

Brooks sees Davis possessing the same qualities as Durant.

“There are great expectations on him on and off the court, and when you’re have to lead at a young age, it’s not always easy to do,” he said. “You have to lead by an example at work, and sometimes you’ve got to be the one that puts an arm around a teammate and get him through something.

“Every player is unique in his situation. But I believe that Anthony Davis is up for the challenge.”

Houston Rockets coach Kevin McHale, who has played with and coached superstars such as Larry Bird and Dwight Howard, was originally skeptical of Davis’ abilities, given his relative lack of offensive output during his one year of college.

“There only a few bigs in this league who can come in and dominate almost from the start,” McHale said. “But Anthony’s work ethic and talent level have shown me he’s only going to get better. If you want to be the best, you’ve got to love to play. And when you’re playing against the other top guys, you’ve got to want to show them you’re better. That’s where Anthony is right now.”

None of this is lost on Tom Benson and the rest of the Pelicans ownership, who are extremely anxious to create for the team the same kind of local passion that exists for the Saints.

Given the team’s uneven history in New Orleans — the move from Charlotte in 2002, two seasons spent in Oklahoma City because of Hurricane Katrina, the franchise being put in receivership and run by the NBA when George Shinn could not financially sustain things, the engineered exit by Chris Paul and finally three straight losing seasons since Paul’s departure — that won’t be easy.

But in Davis, the Pelicans have a player who can be the face of a franchise for a decade — a roundball version of Drew Brees.

“Every team needs a signature player who is synonymous with that team and that brand,” owner/vice chairman of the board Rita Benson LeBlanc said. “It’s not just his ability but his leadership that jumps out at you. Anthony is on a blessed path, and we are fortunate to have him. Is he a Pelican for life? At some point we will have to engage in contract talks with him about that sort of thing, but we certainly hope so.”

Fans are counting on that.

“We’ve been through this with Chris Paul, but AD being a big man can go even further,” said Dwayne White, a season-ticket holder from New Orleans who was wearing a No. 23 T-shirt during the Pelicans’ exhibition game against the Thunder. “They never put together a team around (Paul) that made him want to stay here.

“But if AD can stay healthy and the rest of the young talent jells, we can be going deep into the playoffs. I think people are wondering, if the Saints can win, why not the Pelicans? If they want fans to come out, they’ve got to get those things done.”

As it is, the Pelicans have the ability to hold on to Davis for quite a while.

He’s in the third year of his rookie contact, meaning that next summer they can offer him an extension, which he has until the beginning of the 2015-16 season to accept. The amount can be as much as 30 percent of the salary cap, which is expected to rise significantly thanks to the league’s new media rights deal but will be worth well more than $20 million a year.

Although turning down such an extension is rare, Davis still cannot become an unrestricted free agent until 2018.

Davis politely declines to talk about his contact situation.

“I’m just focused on this season,” he said.

His agent, Arn Tellem, did not respond to respond to interview requests concerning his client.

Along with his income from playing, Davis is developing his portfolio of endorsements, most notably for Nike, Boost Mobile, Red Bull and Foot Locker.

If Davis’ profile seems low compared to some of his peers, it’s only because he deliberately avoided such distractions when he was a rookie to concentrate on developing his game on the NBA level, plus the fact that the Pelicans are hardly a household name nationwide.

Davis’ gigantic likeness may not adorn the sides of buildings — even the Smoothie King Center — like LeBron’s does, but that’s not to say it won’t some day.

“He’s turning into a bit of a pitchman,” Williams said. “But Anthony’s also well-grounded to know that he’s a basketball player first.”

Indeed, Davis does not surround himself with an entourage, relying on his family and teammates for companionship and advice, along with Williams in the latter department.

“I don’t need a bunch of guys around me, because I know what I have to do, and I know what I want to be,” Davis said. “I lean on my coach for a lot of things, but it’s not like there are a lot of other players that I call for advice or other things. There are always going to be demands on your time, but you’ve got to learn when to say yes and when to say no. At the end of the day, it’s the player I want to be and how I want to be looked at that matters.”

That’s not so say Davis isolates himself from others. Far from it.

General Manager Dell Demps tells the story of how, on the day Davis and Williams returned from the World Cup in Spain, Davis came to the team’s practice facility in Metairie where several players were working out — not only saying hello to them, but also taking the time to shake hands with every person in the building.

He also welcomes the things the team has done to improve, most notably trading its 2015 first-round pick to Houston for center Omer Asik to free up Davis to defend farther from the basket.

“Dell and Monty are doing everything they can to win by bringing in a lot of great guys,” Davis said. “Everybody else has worked hard to get better. We’ve just got to stay healthy and get this team rolling like it should be.”

As for himself on the court, Davis displays a complete game, save for 3-point shooting (2-for-15 in his career), going beyond the pick-and-roll specialist who got most of his points around the basket when he entered the league to now hitting 15-foot jumpers when he’s not passing out of double teams.

At the other end, Davis has refined the moves that employ his long reach to disrupt things around the basket, and he remains a sure rebounder. A summer spent with Williams and Chicago coach Tom Thibodeau along with the other veterans has sharpened his already considerable interior skills.

But perhaps the epitome of Davis’ attitude about his game came in the third quarter against the Thunder. A loose ball was bouncing out of bounds, and Davis went two rows deep trying to chase it down. To him, that it happened during a meaningless exhibition game didn’t matter.

“I’m never going to go at it half-way,” he said. “If there’s a chance to make a play, that’s what I’m going to do.”

At the same time, Davis can also welcome a push now and then. Just four minutes into an exhibition game against Houston, he signaled to Williams that he wanted to come out. Williams didn’t comply, and later Davis acknowledged his coach was right, saying it’s all part of reminding him of his desire to excel.

“You want to go out there and play like you’re something special,” he said. “So you try to go out there and play to the best of your ability, go out there and play hard, play for your team, play for the coaching staff, play for the organization.

“That’s what I try to do each and every game.”