Moore, 72, is no longer listed among the coaches on the Colts' website, but the team has made no announcement and declined comment.
Moore, reached earlier this week by the newspaper, also declined to discuss it.
"Nothing," he said. "Not at this time."
Moore has been a coach 48 seasons, 34 in the NFL with five teams, and served as the Colts' offensive coordinator from 1998 to 2009, when he mentored quarterback Peyton Manning and played a significant role in seven successive seasons with at least a dozen victories. He was reassigned as senior offensive assistant before last season, and Clyde Christensen was promoted to offensive coordinator.