The Red Devils have long targeted the former Tottenham forward for a move to Old Trafford.
And it appears United are now trying to land the 28-year-old in the wake of Cristiano Ronaldo’s departure from the Bernabeu.
Juventus sensationally completed the £105m signing of Ronaldo, 33, on Tuesday.
But Bale could still follow the Portuguese out of Madrid as Real undergo huge changes this summer.
Zinedine Zidane has already stepped down as manager after a third successive Champions League title, being replaced by ex-Spain boss Julen Lopetegui.
On the pitch, the likes of Neymar, Kylian Mbappe and Eden Hazard have been targeted in an overhaul of Real’s frontline.
And according to the Manchester Evening News, United want to make Bale the next Galactico to leave the European champions.
Jose Mourinho and Ed Woodward both see the Wales international as the perfect addition to the Red Devils’ attack.
A right-sided forward is wanted, with Mourinho having eyed a reunion with Chelsea winger Willian too.
The MEN say talks over a transfer for Bale have reached an advanced stage.
However, the Real superstar will have the ultimate say on whether he goes to Old Trafford.
Bale is seeking assurances over his position at the Bernabeu.
Despite playing a pivotal role in Real’s 3-1 Champions League final victory over Liverpool, he struggled to nail down a starting spot in Zidane’s team last season.
Lopetegui would need to convince him he is a big part of Real’s plans moving forward.
But Manchester United are eager to sign Bale and are making their stance clear.