United have been heavily linked with a move for the Wales international in recent transfer windows but have so far been unable to prise him away from the Bernabeu, with Madrid previously unwilling to entertain offers.
However, The Mirror reports that the European champions have become increasingly exasperated by Bale's injury record and are now considering cashing in on the 28-year-old.
Bale has recently been sidelined by a calf injury but last week picked up a thigh problem which could keep him out for the rest of the year.
Madrid will now reportedly accept offers of £85m for the winger, who cost Los Blancos a similar amount when he joined from Tottenham Hotspur in a then-world record deal in 2013.
However, United are likely to face competition for his signature from other Premier League clubs, with Chelsea and Spurs also among the interested parties.
Bale has scored 70 goals in 159 appearances for Madrid, helping the club to three Champions League crowns, one La Liga title and one Copa del Rey.