The Reds haven't confirmed the reports.
Chris Heisey replaced Bruce in right field and batted in the cleanup spot.
The move was announced about two hours prior to Cincinnati's home game against Milwaukee, a contest the Reds won in extra innings, 4-3. Bruce was able to pinch-hit in the seventh, swinging and missing at three pitches from Milwaukee reliever Will Smith.
Bruce is batting .216 with three home runs and 14 RBIs in 102 at-bats and was 1-for-4 in Saturday's 6-2 Reds win over the Brewers. His next RBI will be the 500th of his career.
Andy Call is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.