The Cubs are trying hard to trade Matt Garza before Tuesday's 4 p.m. (ET) non-waiver deadline, sources say.

Garza hasn't pitched since July 21 because of what the Cubs described as a cramp in his right triceps. He threw a bullpen session on Monday in Chicago, and the Cubs told reporters it went well.

The Blue Jays and Rangers have been the two teams linked most often to Garza. Foxsports.com suggested the Reds as a possible Garza destination, but two sources described a deal to the Reds as very doubtful.

Garza was at one point considered one of the prize pitching targets on the July market, because of his history of success in the American League East, and because an acquiring team could control him through next season.