Wilson was put on the 15-day disabled list Sunday with right elbow inflammation.
Bell, who entered Wednesday night's game against the Giants with a 3-4 mark, 2.55 ERA and 35 saves this season, was placed on waivers Monday, according to several media sources. The right-hander has fanned 40 and walked 19 while allowing 15 earned runs over 53 innings.
The Padres could withdraw Bell from waivers, negotiate a trade for him or allow him to head to San Francisco for a transfer fee. The Giants have a 48- hour window in which to negotiate a trade for Bell.