The Spanish shot stopper was talked up in the January transfer window with a £50million switch to Real Madrid, and Louis van Gaal is expected to complete a major revamp of his squad in the summer.
The Daily Star recently reported United were mulling over a potential swap deal involving De Gea and Real star Gareth Bale.
It seemed that Real had abandoned their plans to make a move for De Gea after lining up a deal to sign Argentine goalkeeper Augusto Batalla.
But the Daily Mirror claim United are worried they may struggle to retain De Gea's services at the end of the season.
GETTY
Manchester United are worried they could lose David De Gea
It is suggested in their report that discussions over a new deal have been rebuffed.
United are thought to be ready to offer De Gea as much as £140,000-a-week, which should he sign, would make him the Premier League's highest paid goalkeeper.
De Gea, who has been earmarked as a long-term successor to Iker Casillas, sees his current deal expire next summer.
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