At the MLB winter meetings, Brian Cashman says he's confident the Yankees are well in the mix for free-agent pitcher Gerrit Cole. (2:17)

The New York Yankees have offered Gerrit Cole a contract worth more than the record-breaking seven-year, $245 million deal that Stephen Strasburg and the Washington Nationals agreed to Monday, sources told ESPN's Buster Olney.

It is unclear specifically what the Yankees offered to Cole, who also reportedly has attracted interest from the Los Angeles Angels and Los Angeles Dodgers.

"I can't guarantee we're going to wind up with the player," Yankees general manager Brian Cashman said Tuesday at the winter meetings. "I can just guarantee a championship-caliber effort on our part."

Agent Scott Boras said "we're getting far along" in the negotiations and that "numerous offers" have been made by the teams involved. He also said two mystery teams have checked in with him on Cole.

"The Cole negotiations with all clubs are very positive," Boras said "As you can imagine, they're at the ownership level. Everyone's done a real excellent job in their presentations. Well-thought-out processes by all teams, and I think it's something that's given him some great value choices going forward.

"The Yankees and a lot of the other teams that are involved in this; they were all very prepared and did a great job in communicating with Gerrit and [wife] Amy."

ESPN's Jeff Passan reported last week that signing Cole, 29, was the Yankees' top offseason priority and that Cashman has ownership-level approval to offer the right-hander a record-setting deal.

Strasburg's deal with the Nationals surpasses the previous high for a pitcher's contract, set by David Price when he signed a seven-year, $217 million deal with the Boston Red Sox.

Strasburg also has the highest annual average value, eclipsing Zack Greinke's $31.5 million. Both records might not last long, however, given the interest in Cole from the Yankees and other teams.

"I think we all understand and all certainly feel like we have a special group, a special team, that's hopefully in the middle of a chance to do some great things," manager Aaron Boone. "Anytime you're talking about a player the caliber of Gerrit Cole and knowing what he can potentially mean to our club, you know, it's no surprise that we are as invested as we are in pursuing him."

The Yankees' willingness to play in that financial range signals a shift from recent years, in which they have avoided big-money free-agent signings. Their last nine-figure commitment to a free agent was to pitcher Masahiro Tanaka, on whom they spent $175 million in January 2014; he is entering the final year of his deal.

In December 2017, New York traded for outfielder Giancarlo Stanton and assumed $265 million of the $295 million left on his contract.

It wasn't until a January 2018 trade that Cole unlocked the stuff that has him in the conversation for the best pitcher in baseball. In his first season after being dealt to the Houston Astros, he went 15-5 with a 2.88 ERA. This year, at age 29, he was even better: 20-5 with an AL-leading 2.50 ERA and a major league-best 326 strikeouts in 212⅓ innings. He finished second in American League Cy Young voting to teammate Justin Verlander.

Over his seven MLB seasons, Cole has a 94-52 record with a 3.22 ERA and 1,336 strikeouts in 1,195 innings -- his ratio of 10.062 strikeouts per nine innings ranks sixth among active players and eighth all time.