Agent Scott Boras says Gerrit Cole's free agency will be "very different" than Bryce Harper's due to the demand for starting pitchers. (1:01)

The New York Yankees have made signing right-hander Gerrit Cole their clear offseason priority and have ownership-level approval to offer him a record-setting deal, sources familiar with their plans told ESPN.

The Yankees' fondness for the 29-year-old Cole, whose fantastic 2019 season with the Houston Astros set him up to smash David Price's record $217 million contract for a pitcher, was only reinforced during a meeting with him earlier this week, sources said.

New York and the Los Angeles Angels, a team similarly smitten with Cole and in even greater need of pitching, are preparing for a bidding war that executives expect will reach well beyond $250 million, according to sources. The Los Angeles Dodgers' interest in Cole is acute as well, though they are also considering bids for right-hander Stephen Strasburg and third baseman Anthony Rendon, sources said.

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While the expectation going into the offseason was that negotiations with Cole could stretch into January, the clear willingness of teams to engage in high-year, high-dollar deals could ratchet up the timetable, according to sources. Cole's agent, Scott Boras, has yet to solicit offers, but the teams' recognition of Cole's value and understanding of multiple motivated buyers could have an expeditious effect, sources said.

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.

The commitment from owner Hal Steinbrenner to pursue Cole has emboldened the Yankees, who sent general manager Brian Cashman, manager Aaron Boone, pitching coach Matt Blake and longtime Yankees star Andy Pettitte to their meeting in California. The attention paid by New York to embracing modern pitching analysis could appeal to Cole, whose thirst for knowledge and intelligence are among the qualities teams appreciate about him the most, according to sources.

New York finds itself well positioned to absorb the approximately $35 million per year Cole is expected to command. Among Tanaka, J.A. Happ and James Paxton, the Yankees could clear more than $50 million in salaries before the 2021 season. Though a number of their young stars will see escalating salaries through the arbitration process -- outfielder Aaron Judge and catcher Gary Sanchez will be second-time eligible, and infielder Gleyber Torres will be in his first year beyond a near minimum salary -- the Yankees recognize the value of an ace-caliber pitcher such as Cole.

Their familiarity with him dates back more than a decade. In 2008, New York chose Cole with the 28th overall pick in the draft and planned to offer him a record bonus to sign. Cole spurned the Yankees for UCLA and three years later went No. 1 overall to the Pittsburgh Pirates.

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 Astros, he went 15-5 with a 2.88 ERA. This year, he was even better: 20-5 with an American League-leading 2.50 ERA and a major-league-best 326 strikeouts in 212 1/3 innings. He finished second in American League Cy Young voting to teammate Justin Verlander.

Though the Yankees have prioritized signing Cole, they have not ruled out pursuing Strasburg, the reigning World Series MVP who is also being pursued by the Washington Nationals and Dodgers. Strasburg opted out of the four years and $100 million left on his contract with the Nationals and is expected to receive a deal of at least $180 million.