Washington ? Nationals president Stan Kasten acknowledged Saturday there is a “very real possibility” the team will not reach an agreement with No. 1 overall draft pick Stephen Strasburg despite offering him a record-breaking contract.

The Nationals face a deadline of midnight Monday night to sign Strasburg, a right-handed pitcher from San Diego State whose fastball has been clocked at 102 mph.

He is represented by agent Scott Boras, who has the top three players in this year’s draft — all of whom were unsigned as of Saturday afternoon.

“With 48 hours to go, I simply have no idea whether we’re going to be able to reach a deal,” Kasten said in an interview with the Associated Press.

Kasten said the Nationals offered Strasburg more than the record $10.5 million pitcher Mark Prior got from the Chicago Cubs after being the second pick in the 2001 amateur draft.

Washington’s offer came more than a week ago during a face-to-face meeting in California that included Strasburg, Boras, Kasten, Nationals acting general manager Mike Rizzo and team owners Ted and Mark Lerner.

Kasten wouldn’t reveal the exact amount of Washington’s offer nor would he say what, if any, counteroffer Boras had made. But Kasten characterized Boras’ approach as “advocating a new methodology for evaluating draft picks” — changing the way a draft pick’s worth is determined.

“This kid is so impressive. We have nothing but the highest regard for him. If he wants to come and begin his career right now — and do so with the largest contract ever given to any drafted player in the history of Major League Baseball — we can help him accomplish that,” Kasten told the AP. “But if this is more about changing the whole way an industry does business, then we won’t be able to reach a deal.”

Failing to sign Strasburg would be a blow to a franchise that finished last in the majors with 102 losses last season.