The Wales forward has been linked with Real, and their big rivals Barcelona, after a stunning season that has seen him fire in 23 goals for club and country.
Madrid are thought to have made the 23-year-old their number one transfer target, and Bale would no doubt be tempted by a move to the nine-times European champions should they come calling this summer.
Villas-Boas remains confident of hanging on to his man, however. The Tottenham manager today warned Real president Fiorentino Perez he would find it extremely hard to deal with his opposite number Daniel Levy, and believes Bale can realise his aims with Spurs.
"I think for a player to develop to his full potential, it can be done perfectly in this league," Villas-Boas said.
"I think Gareth has that in mind, not only regarding Spurs but regarding this league too.
"We have the best league in the world in my opinion. The best clubs are continuing to attract the best players over.
"We don't want Gareth to go by any circumstances. I have told you in the past that our chairman is very, very difficult to deal with.
"We will try to hold on to our assets. We believe that we have to hold on to the best players in order to achieve our objectives."