Moyes signed a six-year deal with the Red Devils when he succeeded the retiring Sir Alex Ferguson last summer, but the former Everton boss' time at Old Trafford has been cut short towards the end of a hugely disappointing opening campaign which sees the reigning champions currently languishing in seventh place in the Barclays Premier League.
Here are some of the possible contenders to replace him.
Klopp has certainly caught the eye on the European stage in recent years, guiding his dynamic Borussia Dortmund side to the Champions League final in 2012/13 off the back of the Bundesliga titles they won under him in each of the previous two seasons. The German is a charismatic, young coach and would surely prove a popular choice among United fans.
Louis Van Gaal
The Holland coach has a vast amount of top-level experience and success on his CV, having previously been in charge of Bayern Munich, Barcelona and Ajax, and has been heavily linked with both United and Tottenham of late.
Another youthful coach who has rapidly risen to prominence over the past few seasons, former Argentina international Simeone led Atletico Madrid to the Europa League title in 2012 and has overseen their run to the Champions League semi-finals this campaign, while they are also currently leading the Primera Division ahead of Barcelona and Real Madrid.
Blanc won the Ligue 1 title as Bordeaux coach and looks set to secure it again this term with Paris St Germain, having had a stint in charge of the France national team in between. The fact that he spent time at Manchester United at the end of his playing career would likely count in his favour in terms of how he would be perceived by the club's supporters.
There are few players as revered among the Old Trafford faithful as the 40-year-old Welsh midfielder, who is already part of the current United coaching staff on top of being a squad member. There would be considerable goodwill towards him from fans if he were to land the top job, but he lacks management experience. He is set to be appointed as interim manager until the end of the season.
Sir Alex Ferguson
The 72-year-old Scot, who has stayed on at the club as a director since finishing as manager, returning to the hot seat so soon after selecting Moyes to be his successor would certainly be interesting. Whether Ferguson would even entertain the idea is very much up for debate, as is the issue of what his comeback would mean for United in the long-term, given the age-old question of 'how do you replace Fergie?' would be straight back on the agenda. Red Devils fans would take considerable comfort from the sight of their most successful boss in the dugout again, though.