Rodgers left the Welsh outfit in 2012 to take charge at Liverpool, but saw his time at Anfield come to an abrupt end in October.
Current Swansea boss Garry Monk is reportedly coming to the end of his time in charge at the club following Saturday’s 3-0 defeat against Leicester.
The Swans have won just one of their last 11 Premier League games and are just two points off the relegation zone.
David Moyes had been linked with a move to the Liberty Stadium after he was sacked by La Liga outfit Real Sociedad last month, but the Mail claims that Swansea chairman Huw Jenkins is no longer interested in the Scotsman’s services.
Indeed, Jenkins has apparently identified Rodgers as the man he wants in charge, and Monk looks set to be out of the club before Saturday’s clash against Manchester City.