And Real Madrid are reportedly ready to negotiate with the Premier League side over a possible deal for Bale.
It is understood that the Red Devils have been given a boost in their pursuit of Bale, who started the 2017 Champions League final on the bench after missing the last month of the La Liga season with a calf problem.
The Old Trafford club are meanwhile intent on signing another "marquee name" this summer, and have been forced to look elsewhere now that Antoine Griezmann has confirmed he is staying at Atletico Madrid for at least another season.
"In a split second he can win the game for you and I think his manager, Mr Zidane, will fully appreciate that".More news: Mandzukic cracker answers Ronaldo opener in final
Speculation has since increased as many believe Bale could be the high-profile player to leave this summer.
For his part, Bale is known to have told colleagues that Old Trafford is one of the very few destinations he would leave Real Madrid for.
Real president Florentino Perez remains supportive of Bale, but has apparently acknowledged he may have to sell the former Spurs man to afford Eden Hazard or Kylian Mbappe this summer.
We'll have to wait and see how things develop over the coming weeks but this would clearly be a major coup if United could pull it off as Bale is one of the best attackers in the world, despite his frustrating campaign. When Bale signed for Real Madrid, it looked like he would be the flawless replacement for Ronaldo.