Real are reported to be losing patience with the Wales superstar and are prepared to let him leave the club at the end of the season.
Zinedine Zidane wanted to sell Bale last summer but was overruled by president Florentino Perez.
The 29-year-old made huge statement in the Champions League Final, responding to Zidane’s lack of faith by bagging an incredible brace.
The first goal was a stupendous overhead kick which eclisped Cristiano Ronaldo’s stunner in the quarter-final, the second a consequence of Loris Karius’s nightmare game.
Perez’s decision led to Zidane leaving the Bernabeu in the summer.
But there appears to be little chance of Bale following him anytime soon, despite being on United’s wanted list for the last three years.
The Sunday Express understands that Bale is happy living in the Spanish capital and has no plans to return to the Premier League anytime soon.
The news will also be a disappointment to Chelsea and Tottenham who are also keeping tabs on developments and could have rivalled United.
Chelsea are expecting to lose Eden Hazard to Real Madrid in the summer, with the Belgian continually flirting with the prospect.
If Hazard did transfer to Madrid, Chelsea would seek a replacement, with Bale one of the better options available.
Speaking to the media about signing a new Chelsea deal, Hazard said: “I don’t want to say: ‘Yes, I am signing a new contract.’
“And then in the end I don’t end up signing. So I will see.
“Sometimes in my head, I wake up in the morning and think I want to go. Sometimes I think I want to stay.”
The main Achilles heel in Bale’s career has been his injuries, which have led to him never? playing more than 30 league games in five seasons in La Liga.
The winger has fresh injury concerns this international break, too, as Wales prepare to face Republic of Ireland.
Compatriot Aaron Ramsey, who is the subject of some transfer rumours himself, admitted the importance of Bale in the side.
“It’s going to be a blow being without Gareth,” said Ramsey.
“We know how important he is for us as he has scored so many goals.
“But we are looking forward to that test and hopefully we can get back to winning ways.”
Bale left Tottenham in 2013 after a stellar campaign in North London which saw him voted as PFA Player of the Year.
Despite the unbelievable successes Bale has gone on to achieve, his beginnings at Spurs were far tougher.
After coming through Southampton’s famed academy, Bale did not manage to win in any his first 24 appearances for Tottenham.
Now, Bale has won four Champions Leagues and is renowned as Britain’s finest ever sporting export.