Spanish outlet Diario Gol (h/t Sky Sports) reported the Welsh superstar is attracted to Old Trafford as Real consider a fresh swoop for United goalkeeper David De Gea. Los Blancos president Florentino Perez is reportedly willing to allow the winger to switch to the Theatre of Dreams if he can have the world-class stopper in an exchange deal.
De Gea has developed into the best No. 1 in the world, and Real have maintained a long-term interest in the Spanish player.
Bale's poor luck with injuries has seen him consistently stuck on the sidelines, but the Brit remains one of the best on the planet when fit and firing.
The Manchester Evening News (h/t Jack Otway of the Daily Express) recently reported United manager Jose Mourinho is prepared to turn his back on potential moves for Arsenal's Mesut Ozil and Bordeaux's Malcom if he can tempt either Bale or Antoine Griezmann to leave their clubs to join his side.
The surprise capture of Alexis Sanchez has proved United have the motivation to shop at the top tier of world football, and if Bale is keen to move to Manchester, the Red Devils will fight hard to make the transfer a reality.
However, if Real will only sanction a deal with De Gea involved, it could cause a huge obstacle and obstruction.
It will be fascinating to see if Mourinho sanctions the departure of his amazing goalkeeper for a genuine outfield superstar.
De Gea has saved United many points in recent seasons, but Mourinho has been happy with the performances of reserve stopper Sergio Romero when he has started games.
Romero remains No. 1 for Argentina, giving the Special One flexibility if he is ready to trade with the UEFA Champions League holders.
In other United news, Mourinho could be prepared to challenge Chelsea manager Antonio Conte for the signing of Bayern Munich midfielder Arturo Vidal.
German newspaper Bild (h/t Sky Sports) reported Bayern are happy to let Vidal go after finalising a pre-contract agreement with Schalke starlet Leon Goretzka. Vidal has seen countryman Sanchez arrive in Manchester in recent days, and the chance to link up with his fellow international would be tempting.
Vidal has been linked with United multiple times over the years, and the 30-year-old would add more experience to the club's core.
Per Metro, Vidal recently admitted he has no intention of leaving the German champions before the January transfer window closes but will consider his future next summer.
"I'm still here until June and I'm happy," said Vidal. "I hope to win the Champions League and then we'll see what happens, but at this moment I am 100 per cent at Bayern and there is no chance of changing teams."
The midfielder has previously featured under Conte at Juventus, forming a successful partnership with Paul Pogba as the Old Lady dominated Italian football.
However, with Pogba and Sanchez both United players, Mourinho could hold the upper hand in terms of attractiveness.
Here is Vidal in action:
Sanchez's signing will have injected fresh optimism into the Stretford End, but Mourinho needs to continue spending in the summer.
The starting XI has improved in the past 12 months, but United continue to play catch-up as Manchester City flex their muscle on a weekly basis.
Bale and Vidal have consistently featured at the top of European football, and the Red Devils must continue to capture players from this echelon.