The Old Trafford side announced the sacking of Jose Mourinho on Tuesday morning following Sunday’s 3-1 defeat to Liverpool.
The defeat left United trailing their rivals by 19 points, as they sit sixth in the Premier League, 11 points behind fourth-placed Chelsea.
Appointed in 2016 on a three-year deal, Mourinho led the club to second place last season, while winning the EFL Cup and Europa League in 2016-2017 however his time at the club has been overshadowed by clashes with his own players.
A caretaker will take charge of the club until the end of the season, yet SkyBet have priced Rodgers as 16/1 to become the next Manchester United manager.
Former player Michael Carrick and Real Madrid legend Zinedine Zidane are joint-favourites but the Celtic manager is among the next tier of candidates, despite having previously managed Liverpool.
The Northern Irishman has been linked with a raft of jobs down south since arriving at Celtic.