Troy Tulowitzki, the best shortstop in baseball, met with his agent earlier today to discuss whether or not to demand the Colorado Rockies trade him and decided not to demand a trade. The 30-year-old has spent is entire professional career with the Rockies since they took him in the first round of the 2005 amateur draft. While he has missed quite a bit of time to injuries, he has been one of the very best players in the game when healthy, hitting well above league average—even factoring in Coors Fields—and playing very good defense at short.
The Mets could, of course, use a shortstop. Wilmer Flores has not flourished as a hitter yet, and he'd have to hit much better than he has so far this year to make up for his very poor defense at shortstop. That he isn't a major league shortstop is not his fault, as he's not making the decision to play himself there on a daily basis, but if the combination of his hitting and defense continue, the Mets would have to try something else at the position.
That Tulowitzki hasn't demanded a trade right now probably doesn't change the odds that the Mets will acquire him all that much. There's not as much public pressure on the Rockies to make a deal happen, but the team wasn't going to just give him away even if there were. If the Mets were to try to acquire him, there are two major factors in play: the organization's willingness to part with significant prospects and financial ability to take on, presumably, all or most of the rest of Tulowitzki's contract.