A series of reports surfaced on Monday afternoon that the Scot's ill-fated reign as Red Devils boss would shortly be brought to an end, possibly even before this weekend's game at home to Norwich.
It is understood that Moyes is, as things stand, still United manager, but Monday's reports appear to indicate his days are numbered at Old Trafford.
It is believed he could be sacked in the next 24 hours.
Reports cited the 2-0 defeat to Moyes' former club Everton as the final straw for the Glazer family, which owns the club. United, who won the Premier League last season in Sir Alex Ferguson's final campaign in charge, are seventh in the table this time around.
The loss at Goodison Park was United's 11th of a wretched title defence and killed off any last hopes of a return to the Champions League next season with the gap to fourth-placed Arsenal now too big to bridge.
United were knocked out of this season's Champions League by holders Bayern Munich in the last eight, having led briefly in both legs.
They were eliminated from the FA Cup at the first hurdle by Swansea and were knocked out of the Capital One Cup at the semi-final stage by Sunderland.
Moyes continues to paint a positive picture about the future, but he cannot hide from the statistics that show just how badly his first season at United has gone.
United will end the season with their worst points total in Premier League history. They have failed to qualify for the Champions League for the first time in two decades.
And they will only guarantee Europa League football at Old Trafford next term if they overhaul the six-point gap that separates them from Tottenham.
Moyes, speaking to MUTV after the defeat at Goodison, is hoping to end the season on a high with wins in United's remaining four games, but the reports on Monday suggest he may not be afforded the opportunity to even see out the campaign as United boss.
''We need to end the season on a high,'' the United manager said.
''We want to finish by winning all of our games. We'll do everything we possibly can to make that happen.''
Yet another blow hit Moyes on Sunday morning when it emerged that forward Danny Welbeck was considering his future at the club following a lack of game time this year.
The embarrassment among the playing staff at losing yet another game so easily was clear on Monday morning.
Rio Ferdinand, who was not in the squad at Goodison Park, took to Twitter to air his feelings.
''Frustration & disappointment sums up the season so far,'' the United defender wrote.
Juan Mata had started to pay back some of his £37.5million price tag in recent weeks, but the Spaniard had an off-day at Goodison Park.
''I feel very disappointed today,'' United's club-record signing wrote on his personal blog.
''This is how you feel when you spend two weeks waiting for a game, getting ready for it, and then things don't go the way you wanted. It happened in Goodison Park and the truth is this is not the first time, as you know.
''I hate this feeling.
''What the Premiership table shows now is something that neither the club nor the fans deserve.
''I hope the next game comes as soon as possible because, as you can imagine, this bad taste makes me mad.''
Moyes gave a damning critique of his team's defending for both goals, describing it as ''rank'' and ''rotten''.
Leighton Baines converted a penalty to give Everton the lead when Phil Jones inexplicably stuck his arm out to block Romelu Lukaku's shot before Kevin Mirallas slipped through the away back line and beat David de Gea from a tight angle.
Wayne Rooney, captain on his return to Goodison Park, said recent defensive performances have not been up to scratch.
''We conceded two really sloppy goals, which we need to cut out because we're making it hard for ourselves to get back into games,'' the United striker said.
''For the second one, we should have stopped the counter-attack. They ran in behind us. It's not good enough.''
Moyes' Manchester United timeline
Reports on Easter Monday suggested David Moyes was on the verge of being sacked after less than a year in charge of Manchester United.
Here are the lowest points from the Scot's short reign to date.
September 1 - United suffer first defeat under Moyes as Daniel Sturridge gives Liverpool victory at Anfield. Wayne Rooney misses the game with a nasty head wound after being kicked in the head accidentally by Phil Jones in training.
September 22 - Hammered 4-1 at Manchester City. This time Robin van Persie is absent with a thigh injury.
September 28 - United lose 2-1 at home to West Brom, ending the Baggies' 35-year wait for an Old Trafford triumph.
October 19 - Concede last-minute Adam Lallana equaliser against Southampton at Old Trafford.
December 4 - Bryan Oviedo scores four minutes from time as Moyes' former club Everton end their 21-year wait for an away win over United.
December 6 - Rio Ferdinand criticises Moyes' policy of leaving it late to pick his teams, claiming on BT Sport: ''It turns you into a madman.''
December 7 - Yohan Cabaye gets the only goal as Newcastle win at Old Trafford for the first time since 1972.
December 10 - Van Persie suffers thigh injury taking a corner against Shakhtar Donetsk, and is ruled out for seven weeks.
January 1 - Rooney plays in the defeat by Tottenham but is then ruled out for four weeks with a groin injury.
January 5 - Swansea win at Old Trafford for the first time as Wilfried Bony's late goal sends United out of the FA Cup at the third-round stage for only the second time in 30 years.
January 7 - Defeat in Capital One Cup semi-final first leg at Sunderland means a third straight loss for the first time since May 2001.
January 19 - Skipper Nemanja Vidic is sent off as United crash to defeat at Chelsea.
January 22 - United beat Sunderland 2-1 in the Capital One Cup semi-final return leg thanks to Javier Hernandez's last-gasp effort in extra-time but come off worst in an awful penalty shoot-out, with only Darren Fletcher scoring from their five kicks.
February 1 - Stoke end their long wait for a win against United. Charlie Adam's double gives them their first since 1984.
February 7 - Vidic confirms he will leave at the end of the season.
February 9 - United come from behind to lead bottom side Fulham at Old Trafford, but Darren Bent's stoppage-time equaliser settles a 2-2 draw to deny the hosts all three points. Moyes describes the result as being "as bad as it gets".
February 25 - It proves gruesome in Greece for United in the Champions League last 16 as a poor performance sees the Red Devils beaten 2-0 by Olympiacos in Piraeus.
March 16 - Another day United will want to forget in a hurry as two Steven Gerrard penalties and a Luis Suarez strike earns Liverpool a crushing 3-0 win at Old Trafford. It could have been even worse for Moyes' men as Gerrard also hit the post with another penalty.
March 25 - United lose 3-0 to bitter rivals for the second consecutive home league game as a brace from Edin Dzeko and a late strike from Yaya Toure hands Manchester City a derby double. The result ensured United were guaranteed to end the season with their lowest points total in Premier League history.
April 9 - Despite an encouraging 1-1 draw in the first leg and taking the lead through Patrice Evra, the Red Devils go down 3-1 to defending champions Bayern Munich in the second leg of their Champions League quarter-final at the Allianz Arena.
April 20 - Moyes' return to Goodison Park is turned into a nightmare as Leighton Baines' penalty and a goal from Kevin Mirallas give Everton a 2-0 win - a result which confirms United cannot qualify for the Champions League.