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."
Bale's form has seen him compared to Madrid talisman Cristiano Ronaldo as well as Ballon d'Or holder Lionel Messi.
Some critics - Manchester United centre-back Rio Ferdinand among them - have questioned whether Bale should be mentioned in the same breath as a duo widely regarded as two of the greatest players of all time, but Villas-Boas disagrees.
"He is world class and those two players are," the Portuguese said.
"Gareth at the moment is showing that level of form to be at the level of those two players, who have won so much throughout their careers, including European trophies. He still has to achieve that and we hope he can achieve it with us. I think he is very down to earth."
Tottenham will need Bale to be firing on all cylinders come Sunday afternoon when they face Arsenal at White Hart Lane.
Victory for the Villas-Boas' men will move them seven points ahead of their bitter rivals with 10 games to go, but their manager thinks a win will still not guarantee his team Champions League qualification.
"We are on a good run of form and extremely confident, but I don't think (Champions League qualification) is going to be on whatever result happens this weekend," said Villas-Boas, whose side are unbeaten in the league since December 9.
"Seven points is still recoverable for a team like Arsenal.
"It's all very tight still, but obviously we know the importance of the fixture and the way it can impact on both clubs moving forward."
Arsenal have won 14 more north London derbies than Spurs since their first recorded meeting in 1909, but Tottenham have enjoyed more success of late.
Spurs have won three league derbies - the same as Arsenal - in the last five years, and have not lost at home to the Gunners since September 2007, when Bale scored his second goal for the club following his move from Southampton.
But Villas-Boas insists it is too early to say whether the balance of power in the northern half of the capital has shifted Tottenham's way.
"Only through time will we be able to say that," the 35-year-old said. "It won't be because of one season that it has shifted."
Arsenal thrashed Spurs 5-2 in the reverse fixture in November, but Villas-Boas was not helped by the early dismissal of Emmanuel Adebayor against his old club for a reckless challenge on Santi Cazorla.
Jermain Defoe is back from an ankle injury, but may start on the bench.
Should Villas-Boas start Adebayor, he has no concerns about the striker losing his temper again.
"I didn't speak to him," Villas-Boas added. "We've moved on from that incident.
"The player has suffered enough with a three-match suspension."