They have interest in Diamondbacks shortstop Didi Gregorius to play second base in 2014 and potentially replace Derek Jeter in the future, since he won't be a free agent until 2019. He was acquired from the Reds in the Shin-Soo Choo three-team trade that took place exactly one year ago today and was ranked as the 80th best prospect by Baseball America before the 2013 season.
In his rookie campaign, Gregorius, 23, was worth 1.4 WAR, though he only produced a 91 wRC+ and was not rated very highly in the field (-1.0 DRS, -1.0 UZR/150, 13 Errors). While it's only one season, he could have trouble hitting lefties going forward (40 wRC+ against lefties vs. 114 wRC+ against righties). He started off strong, hitting .319/.374/.521 through his first 31 games, however he could only manage a .218/.311/.298 batting line the rest of the season.
It would obviously make a ton of sense to find someone who could be useful now and in the future, since the Yankees don't have many players who are guaranteed to contribute. Gregorius might not be the best choice as primary target; the Yankee lineup currently has enough trouble against southpaws, but if Arizona has soured on him, it's possible they could make a deal, however, I don't know if his value going forward is worth giving up Brett Gardner for 2014, just because it would leave them with Alfonso Soriano as a full-time outfielder.
Another candidate to fill in at second base is free agent Omar Infante, who the Yankees have long been in talks with. It has been reported that he could be looking for a multi-year contract at a rate $8 million per year or higher, so it makes sense to check out the trade market first. There are several teams currently competing for the second baseman, but the Royals seem like they could be the most dangerous if New York really plans to make a run on him.