Stauffer, selected by the Padres with the fourth overall pick in the 2003 Draft, was the longest tenured player on the Padres' roster. He spent most of this season on the disabled list, however, making his lone appearance on May 14 and undergoing surgery to repair tendon damage in his right elbow on Aug. 31.
Stauffer, who was the club's Opening Day starter in 2011, went 23-31 with a 3.94 in 96 games (70 starts) over parts of seven seasons with the Padres.
As for Moseley, his only appearance this year came on April 7. He underwent season-ending shoulder surgery later that month. In his first season with the Padres last year, Moseley went 3-10 despite posting a respectable 3.30 ERA over 20 starts.
Both players could potentially return to San Diego, but it would need to be via Minor League contracts.