SCOTTSDALE, Ariz. — With the Hot Stove League hitting a symbolic benchmark Monday, Brian Cashman aimed high for his close-but-no-cigar Yankees.

“We’re certainly going to be talking to all players,” the Yankees’ longtime general manager said at the first day of Major League Baseball’s general managers’ meetings. “Of course, we’re going to have to talk to [Stephen] Strasburg. We’ll talk to [Gerrit] Cole. We’ll talk to the higher-end guys, clearly, and have conversations there, and we’ll also talk about some surprise guys, I’m sure.

“Our staff will get together, whether it’s dealing with agents, dealing with clubs. It takes two to tango, so it’s hard to predict. Of course anyone would have an interest in players like that.”

Strasburg, the reigning World Series Most Valuable Player for the Nationals, and Cole, the Astros’ ace whom the Yankees drafted in 2008 only to not sign him, top the lengthy list of available free agents. Both are represented by agent Scott Boras, who appeared at the meetings Monday and will meet extensively with club officials the next two days (and address the media on Wednesday).

Other top starting pitchers available on the open market include Madison Bumgarner, Dallas Keuchel, Jake Odorizzi, Hyun-Jin Ryu and the Mets’ Zack Wheeler.

When asked to identify his list of priorities as the offseason begins in earnest, with the Yankees set to meet with other clubs as well as player representatives, Cashman said, “Obviously, starting pitching is always something that we want to continue to look at and shore up. With that said, we still have internal personnel that we’re excited to get up,” at which point he cited Jordan Montgomery, who missed nearly all of 2019 as he rehabilitated from 2018 Tommy John surgery on his left elbow, as well as prospects Deivi Garcia and Mike King.

Cashman refused to delve extensively into questions about the team’s payroll, although it’s apparent the Yankees are willing to exceed the $208 million luxury-tax threshold for 2020. Their appetite for hitting the higher thresholds of $228 million and $248 million, featuring additional penalties, remain to be seen. It should be kept in mind that MLB, knee-deep in tension with the Players Association over offseason spending and efforts, doesn’t want its clubs publicly ruling themselves out for any player’s services.

Cole is expected to be targeted by the Angels and possibly the Phillies, while the Nats and the Padres appear the most likely suitors for Strasburg.

“It’s not as simple as going after it and pulling it down,” Cashman said of the talent available. “There’s a lot of different dynamics.”

While attention naturally turns to big names from other teams in line for big dollars, Cashman acknowledged that he’s engaged in conversations with three of his own free agents. The most simple retention project would seem to be Brett Gardner, who enjoyed an outstanding age-35 season and would like to stay with the team that drafted and developed him — and that needs his center-field prowess in light of the news that Aaron Hicks recently underwent Tommy John surgery on his right elbow.

“We’ve had a longstanding, very successful relationship,” Cashman said of the Yankees and Gardner. “Obviously, we’ll see if that can continue or not. I’ve had several conversations with Joe Bick, which is his representation, but we’ll see. I’m sure there’s a lot of competition.”

Of the shortstop Didi Gregorius, who missed the start of the season while recovering from his own Tommy John surgery and struggled upon his return, Cashman said, “I’ve had several conversations with [Gregorius’ agent] Jim Murray as well. Didi’s obviously been a tremendous player for us. Stepped into some really big shoes there in Derek Jeter and has been an impactful player for us as well.”

Of the reliever Betances, who pitched in just one game due to multiple injuries, Cashman said, “He’s been a tremendous Yankee. … He’s been a homegrown guy, an elite reliever. Difficult season for him. He’s a special person and a great talent. We’ll stay in touch, no question about it.

“It’s hard to improve on a 103-win team,” Cashman said, referring to the Yankees’ regular-season win total. Nevertheless, the GM knows how much his fan base hungers for the jewel franchise’s first title since 2009. And everyone knows that adding a frontline starting pitcher would considerably help that effort.