According to Diario Gol, Bernabeu president Florentino Perez still wants De Gea as he plans a summer overhaul.
And his chances of getting the stopper on-board have improved due to Bale's preference to join United over Tottenham.
Mourinho has apparently got wind of Bale being keen on a move to Manchester and that has softened his stance with regards to De Gea, who he previously refused to let go.
Diario Gol claim Mourinho is willing to negotiate with Real because he believes Bale can return to top form in the Premier League.
GETTY
Gareth Bale would rather join Manchester United than Tottenham when he leaves Real Madrid
David de Gea's stunning WAG taken for a spin in rally car
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De Gea is said to fancy a return to his homeland, while Bale has a pact with Perez to head for the exit door at the end of the season.
Whether United and Real will arrange a straight swap similar to Alexis Sanchez and Henrikh Mkhitaryan's recent moves remains to be seen.
Should a United switch fail to materialise, Bale may be offered as bait to Tottenham to secure a deal for Harry Kane.
The England international is on Perez's wanted list as he seeks to freshen up Real's attack.