It has been widely reported that Jose Mourinho is on the lookout for a long-term replacement for current No.1 Iker Casillas.
De Gea, who has struggled to settle in Manchester since arriving from Atletico Madrid last year, was one name in the frame for a Bernabeu switch.
The 21-year-old has insisted that he is happy at United and not hoping for a move back to the Spanish capital - and it seems like Mourinho is now looking elsewhere.
And reports in Germany have claimed that the La Liga side are ready to pay nearly £30m to land highly rated Bayern Munich keeper Neuer.
The 26-year-old, considered one of the best in the world, only joined in June 2011 but Real think such a big offer would be hard for Bayern to resist.
United, incidentally, wanted to sign Neuer before landing De Gea, after the Germany international's outstanding form at former club Schalke.
But Neuer moved to Munich in a move worth £17m, making him the second most expensive goalkeeper in history at the time.
De Gea then moved to United for £18m - second only to £32.6m Juventus keeper Gigi Buffon as the world's priciest stopper.
Buffon, incidentally, is in talks over a new deal at Juve.