The Yankees, to their credit, do appear to have at least some interest in signing either Gerrit Cole or Stephen Strasburg. To wit, the Yankees will meet with both this week, according to The Athletic‘s Ken Rosenthal. Of course, there’s a difference between meeting with a player and signing them, so Yankees fans would be wise to hold off on the custom-jersey order. 
Connecting every top free agent with the New York Yankees is one of baseball’s longest standing tropes. Sometimes, there’s just no way around it. Take this winter. The Yankees have the clear and obvious need and desire to add a front-of-the-rotation starter, and two of the top three available free agents are aces. Ergo, the Yankees were always going to be connected to them, whether the interest was legitimate or not.
Besides, the Yankees are not presently the favorite to land either. League sources told CBS Sports earlier in the offseason that the Los Angeles Angels are expected to make the richest offer to Cole. (The Angels are also expected to pursue another free-agent starter to pair with Cole in a remade rotation.) Meanwhile, it’s hard to see the Nationals permitting Strasburg to leave town after his dominant postseason. These things can change—and Lord knows they often do—but that’s the current state of the market.
Cole and Strasburg ranked No. 2 and 3, respectively, on our top 50 free agent list. Anthony Rendon, Strasburg’s former teammate, was the only player to rank above them. Either Cole or Strasburg would make sense for the Yankees, who could add them to a rotation that already includes Luis Severino, James Paxton, and Masahiro Tanaka. On paper, that looks like an above-average rotation—albeit one with durability risk across the board. The Yankees might prefer Cole to Strasburg if for no other reason than him having a better track record as it pertains to durability.