Connolly has impressed for the Red Devils since linking up the club in July 2012 after leaving Bolton Wanderers.
He joined Bolton from Wolves in the summer of 2009 as a 17-year-old for a fee of £1million and has been tipped for a big future in the game.
Connolly's career at Bolton stalled, but he has begun to fulfil his potential at Crawley and his progress has not gone unnoticed among clubs higher up the Football League.
Derby County and Charlton are both thought to be admirers and are keeping tabs on him.
The ball-playing central defender made 40 appearances for Crawley this season and he is regarded as one of the best talents outside the top two divisions.
Connolly has one year to run on his current contract at Crawley and his suitors are weighing up moves for the Republic of Ireland Under-21 international this summer.