Spanish journalist Eduardo Inda said on El Chiringuito (h/t Joe Short of the Daily Express) Real president Florentino Perez is aware the Los Blancos squad would be pleased to see the Welshman exit, with the Red Devils ready to trigger a blockbuster move to bring the attacker back to the Premier League.
Inda said he believes United are prepared to pay approximately £100 million for Bale's services, offering the forward a route out of the Spanish capital.
Jamie Jackson of the Guardian recently reported United are ready to spend big in the January transfer window, with manager Jose Mourinho desperate to purchase a forward and centre-back. United have lacked a killer instinct in the attacking third, and have also conceded goals this term due to a weak defensive core.
Per Short, Bale could potentially arrive in January or next summer. Changes in European rules mean players are no longer cup-tied if they feature in the UEFA Champions League for another club.
The sale of Bale would go a long way to the cost of the rebuilding project at Madrid, with ex-boss Julen Lopetegui shown the door after just weeks in charge.
Cristiano Ronaldo's exit was a great opportunity for Bale to claim the Portuguese's crown at the Bernabeu, but the Wales international simply doesn't possess the potency needed.
The 29-year-old has scored just four goals in 12 games in La Liga and the Champions League this term, with Real suffering one of their worst goal droughts for many seasons.
United have seen the acquisition of Alexis Sanchez from Arsenal fail, and striker Romelu Lukaku has lost efficiency since returning from the 2018 FIFA World Cup.
Bale would be a huge shot in the arm to United's chase of a Champions League qualification berth in the Premier League if the Red Devils could complete a dramatic mid-season deal.
The form of Anthony Martial dictates he should keep his starting position if a new player arrives, and Bale has the skill to play as a centre-forward in the correct formation to exploit his talents.
Mourinho has always preferred to buy experienced players who have plenty of success under their belts, making the Welshman the perfect signing for the United manager.
Bale would also sell thousands of shirts, with United executive vice-chairman Ed Woodward always motivated to enhance his club's commercial profile.