And a big-money move for the winger could become a Premier League record, with figures above £50 million being quoted. But is the Argentine, who has been tipped to become United's next no.7, good enough to emulate his predecessors?
Di Maria's current team-mate at Madrid, Cristiano Ronaldo, is arguably Man United's most successful no.7, having taken the Premier League - and Europe - by storm to earn himself a world-record move to Spain.
And the man who wore the shirt before him, David Beckham, also enjoyed success after success at Old Trafford before joining Real Madrid.
The list gets no less daunting before Beckham, meanwhile, with the likes of Eric Cantona and George Best having also frequented the famous no.7 shirt at United. Debates will rage on as to who is the very best.
So how does 26-year-old Di Maria compare?
The Argentine has arguably been overshadowed by Ronaldo at the Bernabeu, although many have suggested he was Carlo Ancelotti's second-most influential player last season.
In terms of flair, however, Di Maria can compete with the very best, possessing speed and skill, perhaps reminiscent of Best. His creativity is also comparable to that of Cantona, while his deliveries can be pinpoint like Beckham's.
In terms of beating his man, the Argentine is no doubt a cut above a Beckham, though his shots from distance surely can't compare to that of Ronaldo.
But the 26-year-old, of course, will be remembered for his achievements at United, not just his abilities. Cantona won four league trophies at Old Trafford, while Best, Beckham and Ronaldo all won European Cups.
By contrast, United are not even in Europe any longer. It is a different time for any new signing to come in. And the fact that Di Maria resembles four iconic no.7s in many different ways means supporters will look to him to get Manchester United back to the big time.