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 on Monday night to sign Strasburg, a right-hander from San Diego State whose fastball has been clocked at 102 mph.

He is represented by uber-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 a major league contract worth 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 — which is why they had the top pick in June's amateur draft — and has the worst record in baseball in 2009, again on pace for 100 losses. Washington also recently lost rookie starter Jordan Zimmermann for at least a year because of a torn elbow ligament.

A year ago, the Nationals had the No. 9 overall pick and selected pitcher Aaron Crow of Missouri, whom they did not sign. Crow went back into the draft this year, was taken 12th overall by Kansas City, and had yet to reach a deal with the Royals as of Saturday.

If there's no deal between Washington and Strasburg, he would go back into the 2010 draft, and the team would be awarded the No. 2 pick in 2010.

Strasburg has been labeled a once-in-a-generation talent. He went 13-1 this season, leading Division I pitchers with a 1.32 ERA and 195 strikeouts. Last month, he won the Golden Spikes Award as the top amateur player in the United States, and was the only amateur on the U.S. Olympic baseball team that won a bronze medal at the 2008 Beijing Games.

"Very, very impressive young man. We'd be very proud to have him as a National," Kasten said. "Very mature. Clearly ready to begin life as a professional. And I hope he signs with us because of that, because I think it really would be a mistake for him to put his career off for another year."

The Nationals executive laid out a scenario in which Strasburg could be in the majors on opening day next season — if a deal were reached by Monday's deadline.

"We think he's not just a draft pick — we think he's a special player, which is why we extended ourselves as much as we did, and will continue to entertain any other issues or concerns he might have in order to get him signed," Kasten said.

But he also said there is a "very real possibility, with 48 hours to go, that Stephen may choose not to sign with us. We remain hopeful. But ... all of baseball history, both long-standing and our own recent history with Jordan Zimmermann, has cautioned us about the risks inherent in signing any young player, particularly pitchers."