For a few years, Kevin Youkilis was one of best players the Red Sox had. He debuted in 2004 but didn't really play full time in the big leagues until 2006. He was good that year, but he was excellent from 2007 through 2011. After Boston's disappointing finish in 2011, Youkilis was shipped out of town in 2012 during Bobby Valentine's one-year nightmare with the team.
Youkilis hadn't been very good early in 2012, but he turned things around a bit after he was traded to the White Sox. For his career, he's a .281/.382/.478 hitter. That's a .375 wOBA and 127 wRC+, but he hasn't reached that level of offensive production since 2011. And after signing with the Yankees for 2013, he was mostly injured and only played in 28 games. He put up his worst single-season hitting stats in the process, too.
Considering he only got a one-year deal before missing most of this season, it's hard to imagine he'll get anything better this year. He'll turn 35 in March, and an incentive-laden one-year deal might make the most sense. The Yankees did not give Youkilis a qualifying offer, which means there's no draft pick compensation associated with him in free agency.
Youkilis has generally split his time between first and third base in his career in the majors, but the Mets don't have a vacancy at third. He'd be an interesting gamble at first if the Mets were ready to give up on both Ike Davis and Lucas Duda, though expecting another Marlon Byrd type of bounce-back might seem too risky for the Mets.
But Youkilis isn't ancient, and trading away one or both of Davis and Duda might free up enough space in the Mets' internal budget to cover most of a deal for him. It's definitely not the most likely of moves, but if Sandy Alderson is looking for relatively inexpensive veterans, Youkilis has one of the best track records among the free agents who fit that profile.