Leonard Fournette is the biggest celebrity on LSU’s campus.

From holding strangers’ babies to taking pictures with 7-month-olds to being approached

by Spanish-speaking students, everyone wants a piece of the sophomore running back. Fournette, after all, is now a 1-to-2 favorite to win the Heisman Trophy — meaning it would be considered an upset if he didn’t receive the honor — and he’s the only Southeastern Conference back to rush for 200 or more yards in three consecutive games.

But when asked during the SEC coaches teleconference Wednesday morning how much better Fournette could be, LSU coach Les Miles didn’t even pause to think about his answer.

“I think he’s just getting started,” Miles said.

If that’s the case, Fournette would likely rewrite the program and national record books. He has already almost broken former Tiger running back Alley Broussard’s single-game rushing record of 250 yards three times, with his closest effort against Syracuse coming up seven yards shy.

The sophomore was only 18 yards from the mark in the 44-22 win against Eastern Michigan last Saturday. But, as always, Fournette didn’t know — or care.

“I wasn’t worried about it. If it comes, it comes,” Fournette said during an impromptu session with the local media Tuesday night. “It’s going to come eventually, I guess. I’m not really worried about breaking the single-game rushing record. That’s not my job. My job is to win.”

Fournette’s Heisman hype has been bolstered by his highlight-reel runs, which showcase his ability to run over, under, around or past defenders. He has broken runs of at least 62 yards in the last three games, and sophomore receiver Malachi Dupre said he expects a big gain from Fournette every Saturday.

“I feel like it’s gonna happen in every game with how good our offensive line is blocking for him,” Dupre said. “...With the explosive ability he has, he can go 70, 80 (yards) on any play.”

Considering the superhuman body of work Fournette has put together in just four games, how can his performances so far be only a sign of better things to come? Miles sees the answer to that question at practice every day.

“He’s never satisfied with where he’s at,” Miles said. “He’s always about making a better cut, recognizing a defensive front and where it generally comes out at. He comes to practice in a good mood and with a like attitude and a smile on his face, but those are things he works to improve daily.”

Injury update

Injured defensive back Jalen Mills dressed out and ran at practice Wednesday, but Miles did not confirm whether he will play against South Carolina this Saturday.

Miles said the senior defensive back “looked pretty good” at practice, and he has been recovering quickly from an ankle injury he suffered during fall camp Aug. 19. A source told The Advocate following Mills’ surgery he would miss at least six weeks.

“I don’t know exactly how much or where (Mills will play),” Miles said. “But there’s probably a chance.”

Senior tight end Dillon Gordon, who has been day-to-day with an Achilles injury he sustained against Auburn on Sept. 19, practiced every day this week.

“We’ll kinda see how it goes,” Miles said.

‘It’s gonna be warm’

Fans will each be allowed to bring one bottle of water into Tiger Stadium for this Saturday’s game. Kickoff is scheduled for 2:30 p.m., and the high for Saturday is projected to be 87 degrees, according to weather.com.

LSU athletic director Joe Alleva said about 75 percent of the usual stadium staff will be on hand for the game, and he’s concerned about its ability to handle the concession stands.

“It’s supposed to be 88 or 90 degrees on Saturday at 2:30 kickoff. It’s gonna be warm,” Alleva said. “We encourage our fans to bring a bottle of water with them and stay hydrated.”

Travel rules

The Tigers will be the visiting team for their showdown with South Carolina in Tiger Stadium. They’ll look like it, too.

The SEC limits teams to a 70-man travel roster for conference road games, and Miles expects that rule will be enforced on LSU despite playing in its home stadium.

“Whatever the restrictions are for visitors, I think we have them,” he said.

Miles said he is unsure if South Carolina can bring and dress as many players as it wants, which teams are allowed to do for home games.

No recruits

The SEC will not allow LSU to host recruits at its game against South Carolina on Saturday despite its relocation to Tiger Stadium. The contest will technically be a home game for the Gamecocks after record rainfall and flooding prompted school officials to move the game from Columbia, S.C., to Baton Rouge.

Normally, invited recruits and their families get to mingle with coaches during pregame warmups.