Joba, Hughes, and Logan will almost definitely be offered arbitration, but Mitre and Moseley are two that might be non-tendered.
Mitre, 29, earned $850,000 last season working primarily as a reliever after losing out on the fifth starter spot last spring (he never really had a chance though). In two seasons with the Bombers he pitched in 39 games over 105.2 innings with a 5.03 ERA. His walk ratio at 2.5 BB/9 wasn’t bad, but his strikeout ratio at 5.2 K/9 wasn’t very impressive.
Moseley, 28, signed a minor league contract with the Yankees last season and was called up in July. He pitched in 16, nine of them starting. Over 65.1 innings he had a 4.96 ERA. He had a worse walk ratio and strikeout ratio than Mitre at 3.7 and 4.5 respectively, but by the end of the season it seemed as if manager Joe Girardi trusted him more.
It’s possible that the Yankees could non-tender both of these pitchers which would make them free agents and then try to re-sign them anyway. The reason for that would be to keep them at smaller deals than they would get in arbitration. They likely would both have to sign major league deals though as they could probably each get guaranteed contracts elsewhere.