There are numerous potential candidates for the huge Premier League role including club legends Cristiano Ronaldo, Nicky Butt, Michael Carrick and Darren Fletcher.
Ole Gunnar Solskjaer is under immense pressure following their 5-0 loss to Liverpool in October and their 2-0 defeat to Manchester City last time out.
His time could be coming to a close as United boss and his odds to be sacked were cut even further when City dominated the Manchester Derby at Old Trafford.
As a result, Rodger's odds to become the next permanent manager at United were slashed, despite reports of Solskjaer being given more time.
The Leicester boss has also been in the spotlight a few times for various Premier League roles including becoming the favourite for the Newcastle job.
Rodgers quickly quashed any possibility of a move to St James' Park though by saying he is focused on the job at hand at Leicester, but it remains to be seen whether a move to Old Trafford could be more tempting.
Zidane has been part of the list of managers to takeover since the Liverpool defeat last month.
But the former Real Madrid midfielder has stated he is 'not interested' in the United job as English football 'does not appeal' to him.
If Solskjaer were to depart it could be in the upcoming fixtures with Watford to play this weekend as United will be expected to keep their top six challenges alive with all three points against Claudio Ranieri's side.
The Red Devils also face a packed schedule from now with the winter football in full swing, including the final Champions League group stage ties against Villarreal against Young Boys.
Solskjaer will be hoping to also thwart more pressure on his role with two games against Premier League leaders Chelsea and just a week later a clash against in-form Arsenal.
Rodgers leads the market well ahead of the ex-Real boss but United's future is uncertain with wavering form.
Other outside chances include current England manager Gareth Southgate and some other former United players are also outside chances with Carrick (33/1), Butt, Neville and Fletcher (66/1).
Cristiano Ronaldo's return to the Red Devils after a decade away has also prompted questions to a potential move to a managerial role.
The Portuguese star has already been seen on the touchlines for United and his odds to be the next man in charge are now 25/1.