No matter what happens with Alex Rodriguez, the Yankees are going to need another third baseman, one who can provide depth on a part-time basis. They can also use a backup first baseman and someone who can take up at-bats as a designated hitter. For these needs, the Yankees have reportedly had internal discussions about the possibility of bringing back Eric Chavez.
After 2012 it was clear that Chavez could still contribute to a major league club, putting together a 126 wRC+ in 113 games, but his 2011 campaign showed just how bad an idea it is to rely on a backup who is just as injury-prone as the player he is meant to replace. In 2013, he showed a little bit of both, hitting at an above-average 114 wRC+, but also only playing 80 games for the Diamondbacks.
He suffered from a strained abdomen, right hip stiffness, and a left knee strain in 2013 alone. He also broke his foot, suffered a concussion, a sprained ankle, and dealt with back pain during his two years in New York. He's essentially more injury-prone than A-Rod.
Though he is billed as a good defender, he had a -10 DRS at third base this season with 2011 being the last time he brought positive value to the hot corner. While he has had some experience at first base, he hasn't been very good in limited action.
At this point in his career, Chavez could be a good DH against righties (123 wRC+), but he has struggled against lefties (86 wRC+). The Yankees don't really need a full-time DH, but a part-time one who isn't really that great in the field anymore might not be the best way to spend money. This could just be due diligence, but the Yankees are definitely better off looking at someone who isn't made of glass.