While Moyes has expressed his willingness to improve the squad, he may also feel the need to clear the decks. With that in mind, here are five high-profile players who could find themselves heading for the Old Trafford exit door before the new Premier League campaign gets underway.
When Evra was part of the United squad that reached three Champions League finals in four seasons, there were not many better left-backs in world football. However, in the last two years, the Frenchman's performances have deteriorated.
While he still looks a threat going forward, the 32-year-old has become somewhat of a liability defensively. Time and again even an average winger was able to get beyond him and send over a cross last season.
What's more, if Moyes is able to land Leighton Baines from his former club Everton, it is likely to relegate Evra to second choice. As we've seen with the France squad at the 2010 World Cup finals, he is not what you would describe as a good squad man.
It is believed that his former club Monaco are keen on him and with their new riches, it may be a tempting way for him to end his career.
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At the age of 29, Fletcher should be at the peak of his powers. In fact, such was his importance to the United midfield that his absence from the 2009 Champions League final against Barcelona was seen as a major reason as to why the English side failed to get to grips with the Spaniards.
Over the last 18 months, though, he has been struck down with ulcerative colitis - a bowel condition.
The Scotland international has recently undergone an operation that is seen by many as his last chance. If successful, he could return to training by the end of pre-season.
However, other sportsmen such as former England rugby international Lewis Moody have previously gone on the record to admit how difficult an illness it is to contend with.
It could be that even before he turns 30, Fletcher is forced to hang up his boots.
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When Anderson arrived at United from Porto aged 18 in 2007, he did so with a lot of promise. Indeed, during his first campaign he won midfield battles against Steven Gerrard and Cesc Fabregas, which prompted the United fans' song about him to the tune of Black Laces's Agadoo.
That season the Red Devils not only won a Premier League and Champions League double, but it also appeared that they had found a player who would go on to be a talisman in their midfield.
Since then, though, the Brazilian has failed to kick on. You would need a calculator to tot up the number of injuries that he has had, while he has not always returned from them in the best of physical shape.
And yet, even when he played last season, he showed at times that he is capable of picking out a decent pass. Even so, it is probably time for a change of scenery and a return to Portugal or even his native Brazil could be in the pipeline.
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Most of the previous statement about Anderson could have been written about Nani. Like his friend and teammate, the United number 17 delivered performances during the 2007-08 campaign that had many believing there was a bright future ahead of him.
To be fair to the Portuguese international, he has been more successful than Anderson. In two of his six campaigns he has returned double figures in terms of goals, while during the 2010-11 season, he made 16 assists.
There is a real sense, though, that he has failed to fulfill his undoubted potential. Granted, he probably has not been helped by those United fans who expected him to take over from Ronaldo, but he has still been far too inconsistent.
As with Anderson, it seems that new surroundings may benefit the winger. Both Monaco and Roma are reported to be interested.
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In his first press conference last week, Moyes was adamant that Rooney is going nowhere. However, the Scot stopped short of saying that the striker is happy to stay.
It may now come across as a sign of weakness if Moyes was to sanction Rooney's departure, but if the 27-year-old does really want out, wouldn't it be better for all concerned if he was granted his wish?
After all, if United do land Thiago from Barcelona, a change of style may be in the offing anyway and it is very unlikely that anyone but Robin van Persie would be the main frontman.
There is also the school of thought that Rooney has simply gone stale at United. The England international may yearn the move for the good of his career.
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