8:14pm: Scott Miller of CBSSports.com hears that Oswalt already has several "very nice offers" on the table, though it's unclear which teams presented them.
3:53pm: The Angels haven't had anyone watch Oswalt throw near his Mississippi home recently, Alden Gonzalez of MLB.com tweets.
11:48am: Rosenthal reports (on Twitter) that neither the Yankees or Tigers are in the mix for Oswalt at this time. The righty intends to sign soon, possibly within the week, and pitch in MLB by mid or late June, Rosenthal tweets.
11:19am: The Phillies and Red Sox occupy last place in their respective divisions, but both teams are eyeing midseason reinforcements. Free agent right-hander Roy Oswalt threw a bullpen session for the Phillies last week and worked out for the Red Sox this week, Ken Rosenthal of FOX Sports reports (all Twitter links).
Oswalt is also throwing for two unknown teams, Rosenthal reports. Jon Heyman of CBSSports.com hears from someone who expects Oswalt to return within a month (Twitter link).
The Phillies, winners of five consecutive games, are familiar to Oswalt, who pitched for Philadelphia in 2010 and 2011. The Red Sox, who have won six of their last seven games, expressed interest in Oswalt last offseason after the Phillies declined his 2012 option. The 34-year-old appeared to be in good shape during his workouts but was not yet in midseason form, Rosenthal reports. Bob Garber of Select Sports Group represents Oswalt.
Mike Axisa contributed to this post.