The Red Devils have long targeted the former Tottenham star.
And Jose Mourinho revealed his interest in Bale during the summer when United played Madrid in pre-season.
The Wales international, 28, has endured a tough relationship with fans at the Bernabeu.
And injuries have plagued Bale in recent years, meaning Madrid could be ready to offload him.
The Mirror claim Mourinho and Manchester United executive vice-chairman Ed Woodward are excited at developments over Bale’s future.
The duo believe they will have their best chance ever of finally landing Bale at the end of the campaign.
Madrid will want to recoup what they paid for the £85m superstar forward.
But the Mirror crucially add the La Liga giants may demand Spain’s No.1 as part of any deal.
De Gea could hold the key to Bale joining United, leaving Mourinho in a dilemma.
The Portuguese won’t want to lose his world-class goalkeeper, but would consider the arrival of Bale a game changer.
De Gea, 26, is said to have told friends he wishes to play for Madrid at some stage in his career.
He is happy in Manchester, but in order for Mourinho to get Bale, De Gea may move on next summer too.
Mourinho feels the time is right to sign Bale, with United looking to become a recognised force in the Champions League once again.
