Entering the 1946 season, Rocco was competing with Les Fleming and Eddie Robinson for the starting first baseman job. Fleming won the job and held it, though Rocco saw occasional playing time until June 26, when he was traded with cash to the Chicago Cubs for first baseman Heinz Becker in one of new owner Bill Veeck's first moves. However, Rocco refused to report the Nashville Volunteers, the Cubs' minor league organization, and considered quitting the game, which put the trade on hold. He eventually did report to Nashville, and finished the year having played 34 games in the majors and 37 games in the minors. After the season the Boston Red Sox signed him to a contract as a potential backup first baseman, but he did not make the cut, and was sent to the Seattle Rainiers of the Pacific Coast League just before the 1947 season started.