San Francisco Giants
The Giants are very much playing in the deep end of the free agent pool this offseason. They are among the top suitors for Yoshinobu Yamamoto and have been very public about their desire to try and sign Shohei Ohtani. Even if they miss on both of those guys, their pursuit of them shows that they have money burning a hole in their pockets and seem to be very keen to add a higher end starter.
Assuming a world where they miss out on Yamamoto and Ohtani which is very possible, the Giants are likely to be aggressive in going after the next tier of free agents. What the Giants really need is an impact bat or two, but this market is awful in terms of position players and clearly the Giants don't mind target an arm right now. If pitching is the strength of the market (and it is), expect the Giants to be involved with the better arms and that definitely includes Gray who has the added benefit of probably being cheap enough to keep the Giants in the running for other good free agents.
The problem for the Giants is that Gray may not look at that team and think "contender". Both the Dodgers and the Diamondbacks look like they are in much better spots than San Francisco right now and the Padres are going to be a wild card once again and that is just in the National League West. Until the Giants can assemble a lineup that looks like it can at least be reasonable, an older guy like Gray isn't going to be enamored with the possibility of finishing out his career playing on a team that looks more like a .500 club than a playoff contender.
Money talks, though, and the Giants have plenty of it to make any attempts to sign Gray that much harder.