David Moyes, the Manchester United manager, has as few as 12 games to demonstrate to the Glazer family that he is the man they should trust with a £200m summer transfer kitty, to fulfil their aim of winning the Premier League next season.

Though the club's owners retain full confidence in Moyes, the defeat at Olympiakos in the worst performance of his seven months at the helm appears to have changed the mood about the manager's capacity to turn around the situation at Old Trafford. United have not contemplated changing manager this summer, with the expectation being that Moyes will have set United on course by the next campaign. But he is not immune to dismissal if there is a downward momentum between now and May. The fall-off in performances – United have taken 45 points from 27 Premier League games this season compared with 68 from 27 last season – is on a scale the club had simply not anticipated.

Tuesday's defeat in Athens prompted a rush of rumours of Moyes' departure to spread across social media. They were false, though several more bad results could leave Moyes in a very vulnerable position, with United facing Liverpool and Manchester City at home in a nine-day spell next month. Those games fall either side of the Champions League last-16 home leg against Olympiakos in which United must repair a 2-0 deficit after this week's dismal away-leg display. Moyes has 10 weeks to satisfy the Americans that he is the man to rebuild United into a side who can challenge for the title next season.

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The club, who are privately resigning themselves to a season out of the elite European competition, will launch into the transfer market this summer with a pitch to prospective new players that winning the Premier League – rather than merely regaining a top-four place – is their ambition for 2014-15. Potentially there could be six new recruits in a pivotal four months of business. The situation is complicated by the World Cup but the club hope that business for German or Spanish players could be completed before that tournament.

United harbour some hope that Patrice Evra's obvious affection for the club – manifest in him being one of the best performers this season – may persuade him to stay and share responsibilities with a new, younger left-back. The club anticipate competition from Chelsea and Manchester City for Southampton's Luke Shaw. Bayern Munich's Toni Kroos has been a target but United will not allow themselves to be used as a bargaining tool to engineer better contracts for other clubs' players.

Moyes will also be asked to develop the players he already has, as United's board feel that the "churn" of seven players coming in and going out has the potential to alter the dressing-room dynamics, leaving the manager with too much integration to contend with early in the season.

Wilfried Zaha may return to United from his loan spell at Cardiff City, despite his limited chances so far. The problem this season has been the lack of games which he could be thrown into from the bench. Too much has been riding on too many games.

Moyes will only stay if the club's owners believe he has the capability to turn a £200m investment in players into success on the pitch. One of the most disquieting aspects of the last month is that United do not seem to be improving despite the return of the Robin van Persie/Wayne Rooney partnership after injuries and the addition of Juan Mata to the ranks. Many of the players in Moyes' squad – including Tom Cleverley, Shinji Kagawa and Danny Welbeck – appear desperately short on confidence.

United came under fire over emails warning season-ticket holders who had not met their obligatory payment for the Olympiakos home match in three weeks that they would be refused their season-ticket entrance for the Manchester City home game if they didn't pay up.

The timing, 24 hours after the defeat in Athens, was unfortunate though those fans do owe the club for the Champions League tie and the course of action taken to secure payment was standard.

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