According to Le 10 Sport, Manchester United would be willing to offer up to €110m for the Welshman, €19m more than Real Madrid paid Tottenham for his services in 2013.
The report claims that while Bale has been a huge success at the Bernabeu, helping the club to its 10th Champions League trophy, there's a feeling that he's not essential to the club long-term.
If Real Madrid can make a profit on Bale and bring in Eden Hazard from Chelsea for a significantly smaller transfer fee, Real Madrid could be comfortable letting the former-Spurs star go.
A sale would allow Madrid to secure several squad players without demonstrably weakening the club's squad - after all, they would still have Cristiano Ronaldo, Isco, Karim Benzema and James Rodriguez, as well as potentially Hazard.
Manchester United have been long-term admirers of the Welshman since his days as a teenager at Southampton playing in the Championship.
They were also heavily linked with Bale before he left White Hart Lane for the Bernabeu, but could not compete with the Spanish giants at the time.
Now though, Manchester United are spending big to make sure they regain their place in the Champions League next season. They spent around £150m over the summer, including a British record £60m on then-Real Madrid attacker Angel Di Maria and they're expected to be active in January and then next summer again.