The Argentine is believed to have a bleak future at the Bernabeu, with Gareth Bale suspected to be on the verge of completing his world-record move to the Spanish capital.
As a result, Los Blancos are open to selling, which has alerted the Premier League duo.
United are long-term admirers of Di Maria, and even rivalled Real for his signature in 2010.
They have since remained keen on the South American, and could step up their pursuit in the coming days as David Moyes pushes to bring in his first notable signing of the summer.
Arsenal are also interested, with Arsene Wenger said to be desperate to draft in a big name to ease the growing concern among supporters of the club.
So far the Gunners have only managed to agree a deal for French youngster Yaya Sanogo during the transfer window, and have missed out on Luis Suarez and Gonzalo Higuain.
French giants Paris Saint-Germain are another side interested in his signature, but a move to England could be more appealing top Di Maria.
Meanwhile, Real are also willing to listen to offers for Tottenham target Fabio Coentrao.
Arsenal and Manchester United fans, would you like to sign Angel Di Maria?
Tell us your thoughts below!
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