STAMFORD, Conn. -- While Brian Cashman was descending the Landmark Building on Friday in preparation for a holiday celebration this weekend, the New York Yankees general manager came across a message taped to a 10th-floor window from a fan: Please sign Gerrit Cole.

Cashman confirmed he met with Cole in California on Tuesday and spoke with free-agent pitcher Stephen Strasburg the following day.

"It was a great opportunity, clearly it was very public, that we met with Gerrit Cole and Strasburg while I was on the West Coast," Cashman said. "At least, that's who you all are aware of so far. Who knows who I met with?

The Yankees have made signing Cole their clear offseason priority and have ownership-level approval to offer him a record-setting deal, sources familiar with their plans told ESPN's Jeff Passan on Thursday.

Cole and Strasburg are the top pitchers on the free-agent market. The Yankees would like to add an ace to a rotation that already includes Luis Severino, Masahiro Tanaka, James Paxton and J.A. Happ.

Along with Cashman, assistant GM Mike Fischman, manager Aaron Boone, new Yankees pitching coach Matt Blake and former Yankee pitcher Andy Pettitte made the trip to speak with both pitchers, who are represented by Scott Boras.

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 the meeting, sources told ESPN.

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 Strasburg and third baseman Anthony Rendon, sources told ESPN.

Cashman offered little about possibly signing either player, declining to discuss how much the Yankees might spend.

"I think it was an important part of the process for them," Cashman said. "It sounds like they have met with many teams, and obviously I can't predict the future or the timing of their futures, only really they control that."

Cole was 20-5 with an AL-best 2.50 ERA and a big league-high 326 strikeouts this year for the AL champion Astros. He was originally drafted by the Yankees with the 28th overall pick in the 2008 MLB Draft, but he declined to sign a contract and opted to attend UCLA.

Strasburg was the MVP of the World Series for the Washington Nationals and was the organization's first overall pick in the 2009 draft.

Cashman will return to California for the baseball's winter meetings, which begin Monday. First, he'll attend Sunday's Heights and Lights, where he will dress as an elf and again descend the Landmark Building.

"Obviously, I'll be flying back out after this event and in the meantime staying engaged," said Cashman, who declined to say if another meeting with either pitcher was planned.

"I'm open to do clearly whatever, as always, is important for the Yankees. If there are certain steps that need to be taken, or conversations on the phone, like any club we are fully prepared to do what's necessary."

The Associated Press contributed to this report.