This is according to the Manchester Evening News, who claim De Gea was unhappy that Mourinho stated the goalkeeper was sleeping towards the end of the 0-0 draw with West Brom.
West Brom almost snatched a win at Old Trafford earlier this month after De Gea dropped a speculative Darren Fletcher effort late on.
But luckily for Manchester United the ball bounced off the crossbar to keep the game goalless.
Manchester United star David De Gea is unhappy with Jose Mourinho
After the match Mourinho said: "David De Gea was sleeping and he did the funny thing at the end.
"I was laughing with that."
De Gea missed the 3-0 win over Sunderland on Sunday, and will not face Anderlecht tomorrow (8.05pm) in the Europa League.
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Jose Mourinho said David De Gea was sleeping after the draw with West Brom
The Spaniard has been heavily linked with a switch to Real Madrid in the last few months with Zinedine Zidane keen to make him his new No 1.
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De Gea came close to joining Real in the summer of 2015 but a deal broke down in the final hour.
Real are set to renew their interest at the end of the season though and are likely to test United’s resolve with a bid.