Jennings injured his finger while sliding during the Rays' win over the Giants Saturday night.
Jennings was hitting .258 with 11 home runs, 40 RBIs, 17 stolen bases and 69 runs scored in 104 games this season.
Bourgeois was hitting .291 with two home runs and 57 RBIs in 84 games for the Bulls this season.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.