The French side want to sign a marquee name this summer and had hoped to lure the Welshman away from the Bernabeu.
But Bale will only consider a return to the Premier League and more specifically United.
Spanish outlet Don Balon say the former Tottenham man is fed up with Cristiano Ronaldo and his ongoing tax issues in the country.
Bale is also unhappy with Florentino Perez who believes Marco Asensio is the new star in Madrid instead of the 27-year-old.
The winger was initially sceptical about working with Jose Mourinho but he is now confident he can overcome that obstacle, according to the report.
United’s financial position makes a deal possible with Bale’s mind made up.
TRANSFER NEWS LIVE: All the latest gossip, rumours and done deals
The Wales star has enjoyed huge success since leaving Spurs for Real back in 2013.
Bale has won the Champions League three times, La Liga, the Spanish Cup and the Club World Cup.
United are desperate to overhaul their squad as they prepare for a return to the Champions League and look to challenge for the Premier League title this season.
The Red Devils have already signed centre-back Victor Lindelof from Benfica and are closing in on Nemanja Matic and Bale’s team-mate Alvaro Morata.
