Despite reports that the Red Devils' owners are continuing to back Moyes, it's believed concerns remain over the Scot's ability to turn things around after a dreadful debut campaign at Old Trafford.
United have endured their worst season of the Premier League era under the management of the former Everton boss, who Sir Alex Ferguson strongly recommended after announcing his retirement at the end of last season.
A tally of 57 points after 33 matches leaves the reigning Premier League champions seventh in the table, and faced with an uphill struggle to secure qualification for next season's Europa League.
For the first time in 18 years, meanwhile, Manchester United will not compete in the Champions League group stages - which will have a negative impact on the club's finances over the coming months.
The Glazer family are keen to ensure that Moyes, who signed a six-year contract last summer, is the man to take the club forward before handing him a transfer kitty in excess of £100m.
However, reports claim that Manchester United officials recently met with Netherlands coach Louis van Gaal, fuelling speculation that the Red Devils may opt to sack Moyes before the start of the 2014/15 campaign.
Manchester United fans: should the club sack Moyes this summer? If so, who should replace him?