It is reported that the club has refused to deny the rumours.
Moyes was chosen by Sir Alex Ferguson to succeed him at Old Trafford after 26 years. During Ferguson’s time at the helm, United dominated the English game which included them winning 13 league titles, two European Cups, five FA Cups and four League Cups amongst other trophies.
It was always going to be a hard act to follow for any manager, but Ferguson opted for the man that led Everton from the brink of being relegated from the Premiership to consistently fighting for European places.
It is believed that Ryan Giggs will take over first team affairs should Moyes depart Old Trafford before the end of the season.
It has been a difficult campaign for the Scot as the side currently languishes in seventh place in the league table, and with no silverware to come from this season.
Moyes has been criticised for his style of play after he was awarded a six-year contract at Old Trafford, but also the manner of the defeats.
Some have said clearing out the backroom staff and bringing in his own team was a big factor.
So far in the league this season, United have lost 11 games but the manner of their defeats has been a massive factor. Humiliating defeats at home to fierce rivals Liverpool and Manchester City have been lows but Everton, Newcastle United and West Bromwich Albion have all left Old Trafford with three points as well.
It has been said that Manchester United have also refused to deny rumours over whether they are parting company with Moyes.