Ben Zobrist is the Mets' number one target, according to Ken Rosenthal. Having spent his entire major league career with the Rays, Zobrist was traded to the A's before the 2015 season and traded by the A's to the Royals shortly before the trade deadline in July.
Know for his bat and defensive versatility, the 34-year-old hit .276/.359/.450 with a 123 wRC+ in 126 games in the regular season. He spent the majority of his time in the field playing second base, with significant time in left field and a few games at right field and third base. He has played a bit of shortstop over the course of his career, but he did not play the position this year. He was worth 2.1 fWAR, his lowest single-season mark since very early in his career, primarily because of a huge swing in the assessment of his defense.
A switch-hitter, Zobrist has been better against left-handed pitchers but has hit well against right-handed pitchers, too. He doesn't have any draft pick compensation tied to him, as he was traded mid-season and therefore ineligible for a qualifying offer. He played well in the playoffs and hit .303/.365/.515 in 75 plate appearances.
The Mets have a vacancy at second base, of course, as Daniel Murphy is a free agent. Murphy declined a qualifying offer from the Mets. They also have two left-handed-hitting starting outfielders in Michael Conforto and Curtis Granderson, which might make Zobrist's ability to play the corner outfield spots a little more appealing.
The downside with Zobrist is his age. Next year will be his age-35 season, and Zobrist is said to be seeking a three-to-four-year contract. The Mets have some competition in trying to sign Zobrist, too, as Ken Rosenthal's report mentioned that Nationals, Braves, and Giants are among the other teams attempting to do so.