Carlisle have started their search for a new manager after they parted company with long-serving boss Greg Abbott on Monday.
The League One side decided to axe Abbott following their poor start to the season and they are now keen to bring in a new man to turn around their fortunes.
Sky Sports understands Coleman has thrown his hat into the ring and is interested in succeeding Abbott at Brunton Park.
Coleman has been out of work since leaving Rochdale in January and he is keen to get back into management.
The 50-year-old worked minor miracles at Accrington, taking them from the Northern Premier League First Division back into the Football League and guided them to the League Two play-offs in the 2011/12 season.
The Liverpool-born boss achieved his success at Accrington, despite working on a shoe-string budget and his work caught the attention of League One Rochdale.
Coleman's sides have always been known for their attacking brand of football and his ability to help develop young players would make him an attractive proposition to Carlisle.