Nearly every Major League Baseball team has called Trey Dawson.

The highly touted shortstop and LSU commitment has told all of them the same thing: Pay me this much, or I’m enrolling at LSU.

“We’ve told them the number,” Dawson said Tuesday from his home in West Virginia. “We’ve told them, ‘We’re not going for a penny less than that.’ ”

It’s that time of year again: The MLB draft begins at 6 p.m. Monday and runs through Wednesday.

Draft-eligible LSU players, high school prospects who have committed to the Tigers and coach Paul Mainieri and his staff are all squirming in their chairs as the draft approaches. It might be toughest for coaches who are hoping their star-studded recruiting classes remain intact as pro teams hurl six- and seven-figure signing bonuses at teenagers.

“It’s a pain,” Mainieri said.

And it’s often drawn out. Draftees have until July 17 to sign.

Of LSU’s 16-man recruiting class in 2015, four prospects are potential risks to bypass college and sign with a club because of their lofty stature among pro scouts: right-handed pitcher Jacob Taylor from Picayune, Mississippi; right-hander Cole McKay from Spring Branch, Texas; Dawson; and one of the late additions to the group, infielder Mitch Piatnik of State College of Florida community college.

None are considered first-round material, but McKay (No. 89) and Taylor (No. 77) are ranked in MLB.com’s latest top-100 rankings of draft prospects. Taylor and Piatnik, as junior-college players, may be more willing to sign.

LSU has four potential underclassmen who could bypass their senior years for pro ball: shortstop Alex Bregman, first baseman Chris Chinea and outfielders Mark Laird and Andrew Stevenson.

Mainieri expects to lose all four juniors to the pros. Bregman is in line for a top-10 selection and a signing bonus of more than $3 million. Stevenson was ranked as one of the top 30 college prospects by D1Baseball.com and could go as high as the top three rounds — in line for a bonus of more than $500,000.

The draft didn’t interfere with LSU’s postseason last year since the Tigers lost in the regional round. It’s a different story this season.

“It’s an anxious time while we’re still in the midst of us making a run for a national championship, having to deal with this,” Mainieri said. “It’s difficult to balance the two things. It’s an important thing in their lives. They’re about to fulfill their dream of playing professional baseball.”

But what about the future — those LSU recruits?

“It’s a crapshoot,” Mainieri said. “We want players good enough to win with, but sometimes those players who are good enough to win with are a risk for the pro draft. We try to do our homework and see what the kids are thinking. Sometimes you take chances on high-end kids. Sometimes it works.”

Mainieri is hoping it works as well as it did last season. The Tigers lost just one member — infielder Bobby Bradley — of a 12-man recruiting class ranked No. 1 in the nation. Mac Marshall, one of the most highly rated pitchers in the nation, later left the program, too.

Still, the Tigers kept a host of highly rated draft risks, including pitchers Alex Lange, Doug Norman, Jake Latz and Jake Godfrey and catcher Michael Papierski.

Latz passed on nearly $1 million to come to school. Would Dawson, McKay, Taylor or Piatnik do the same?

Dawson wouldn’t reveal the figure he told major league clubs, but it’s likely at least $1 million. He’s a guy LSU might count on next season.

The Tigers are likely losing their All-America shortstop, Bregman. He said LSU coaches have told him that their expectations for him are “really high.”

“They’re expecting a lot from me to come in and have a big impact on the team,” Dawson said. “It’s going to take a lot for me not to go to LSU. They know the situation. They know LSU is the top program in the nation. It takes a lot for anybody not to go there.”

Said Andy Cannizaro, LSU’s recruiting coordinator and hitting coach: “Life-changing money is different for everybody.”

For instance, Latz passed on that bonus last year while Bradley signed for about the same amount. Dawson has been in constant contact with Mainieri and Cannizaro over the past few weeks.

The coaches have offered the prospect “the benefits and non-benefits” of both signing with a pro team and enrolling in school, he said.

“Like I tell the players, don’t let everybody convince you this draft is a once-in-a-lifetime opportunity,” Mainieri said. “It’s once-in-a-three-times-in-a-lifetime opportunity. You’re eligible out of high school, after your junior year and after your senior year. Going to LSU is a once-in-a-lifetime opportunity.”

Cannizaro has been on the opposite side of this ordeal. Just a year ago, he was completing his fifth year as a scout for the New York Yankees. Now, he wants high schoolers to pick college, not the pros.

There’s a bonus in going to school, Cannizaro said.

“You love taking kids from the SEC and from LSU. It gives you the opportunity to see them perform on the biggest stage they’re going to be on before the big leagues,” he said. “You get to see talented kids perform in pressure situations, against quality pitching and in big league park-type atmosphere.”

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Potential top-10 round draft picks

Player

Position

Top 200 prospect ranking*

Seniors

Kade Scivicque

C

NR

Conner Hale

3B

NR

Jared Foster

2B

NR

Zac Person

LHP

NR

Juniors

Alex Bregman

SS

4

Andrew Stevenson

OF

79

Chris Chinea

1B

NR

Mark Laird

OF

NR

2015 recruits

Jacob Taylor

RHP

77

Cole McKay

RHP

89

Mitch Piatnik

INF

NR

Trey Dawson

INF

NR

*MLB.com

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2015 LSU recruiting class

RHP Cole McKay, Spring Branch, Texas (Smithson Valley)

LHP Nick Bush, Leesburg, Georgia (Lee County)

RHP Caleb Gilbert, Hoover, Alabama (Hoover)

INF O’Neal Lochridge, Lafayette (St. Thomas More)

OF/LHP Brennan Breaux, Lafayette (St. Thomas More)

INF Trey Dawson, Hurricane, West Virginia (Hurricane)

INF Brody Wofford, Rome, Georgia (Model)

OF Antoine Duplantis Lafayette (Lafayette)

C/INF Chris Reid, Baton Rouge (St. Michael)

OF Cody Ducote, Kenner (Brother Martin; Delgado CC)

1B Brice Adams, Baton Rouge (Dunham; Delgado CC)

INF Cole Freeman, Mandeville (Lakeshore; Delgado CC)

C Jordan Romero, Baton Rouge (Catholic; LSU-Eunice)

RHP Jacob Taylor, Picayune (Picayune; Pearl River CC)

RHP Riley Smith, Lufkin, Texas (Hudson; San Jacinto College)

INF Mitch Piatnik, Winter Haven, Florida (State College of Florida)

Follow Ross Dellenger on Twitter @DellengerAdv.