The £59.7million signing has seen his form fade in recent months, and it is believed a number of top European clubs including Paris Saint-Germain are monitoring his situation.
Louis van Gaal is widely expected to carry out a major overhaul of his squad in the summer, and he could be handed a whopping £150million to splash out on player recruitments.
And according to The Sun, Di Maria's days at Old Trafford could be numbered.
They claim the Argentine was blasted by Van Gaal for his performance after coming on as a substitute in the 2-1 win over Liverpool on Sunday.
It is thought Di Maria wasn't too happy at the dressing down given by his manager.
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Angel Di Maria could be set to leave Manchester United
Obviously I need to find a place where I have continuity and where I can play
Radamel Falcao
Di Maria's potential exit could also precipitate Radamel Falcao's possible departure.
Falcao admits he may have to leave Old Trafford in order to get more regular football under his belt.
"When the championship finishes, of course I will sit down, analyse things and decide what is best for me," he told Colombia's Radio Caracol.
"Obviously I need to find a place where I have continuity and where I can play.
"I am totally focused on the club. There are eight games left and anything can happen."
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