Why the Mets haven't offered him a deal
While Nimmo has proven to be a very productive offensive player when in the lineup, he has had trouble staying on the field thus far in his major league career. He has struggled with injuries the last few years, and he also was only a part-time player early in his career. So, despite showing flashes of elite upside, he hasn't proven that he can be relied upon day in and day out yet.
According to Baseball Reference, Nimmo's career high in games played was in 2018, when he played 140 games. If the Mets get 140 games out of him this year they will likely be ecstatic, and it's much more likely they are interested in bringing him back long-term come the offseason. However, aside from 2018, last year was the most games he played in a season, and he only played in 92. And then after that he hasn't played in more than 70 games in any other season in his career.
So, while he has shown that he is the type of offensive piece the team would like to build around, his durability is a concern. He has only played a full,162 game season once in six years, and has missed significant time in nearly every other season. Obviously, 2020 is tough to judge because he did only miss 5 games that season, but the season was shortened to 60 games as a result of the global pandemic, so it is tough to gauge whether he could've stayed healthy the whole year, but also impossible to knock him for that because it was out of his control.
Add to that the questions of where he truly belongs defensively in the outfield, and it is easy to understand why the team would like to see him prove himself before talking a long-term contract. He has been a primary left fielder for much of his career, but has recently been playing more in center field, which is where he will play this year.