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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?