Marca reports that Di Maria wants to stay and coach Carlo Ancelotti wants to keep him.
But Real Madrid directors could be interested in raising around £34million by selling him once they sign Tottenham star Gareth Bale.
United and Tottenham have also been strongly linked with Real Madrid left-back Fabio Coentrao.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.