Yamamoto has had multiple meetings with the Mets with Cohen's wallet still open
Despite the fact that the Mets have declared very publicly that they are not looking to push for contention until 2025, Yamamoto's free agency is a case where signing him now would set the Mets up nicely for when they expect to compete again. Mets owner Steve Cohen clearly has the money to sign Yamamoto and locking him up now would help solidify their plans as well as their rotation going forward.
Right now, the Mets are among the favorites to land him. Cohen flew to Japan to meet with Yamamoto before he began his tour of team meetings in the states and have met with him a second time since then. Money will be no object if Cohen wants him, so finances aren't going to be what costs the Mets if they lose out on Yamamoto. The only question is whether or not Yoshinobu believes that the Mets will be able to field a playoff contender in the next couple of years.
The Yankees are still favorites to sign Yamamoto
If you are a looking for a betting favorite to sign Yoshinobu Yamamoto, look no further than the Yankees. The Yankees are MLB's biggest global brand and they play in the biggest market which has to be very appealing. In addition to that, they are highly motivated to push their chips in given that they just traded for Juan Soto and they may only have him for this year given his contract status and the fact that Scott Boras is his agent. Given all of that, they are the frontrunners for Yamamoto at the moment.
The Yankees have the money to meet Yoshinobu's contract demands, they are certainly motivated to land him, and they have the drawing power as an organization that few teams possess. After multiple meetings with Yamamoto's team, New York is optimistic about their chances to snag him. If they pull it off, things could get very exciting very quickly as the Yankees will instantly become a top playoff contender going into 2024.