The Wales international forward, who added the Football Writers' Association award to his PFA double on Thursday, is one of the most sought-after players in world football having drawn interest from various clubs throughout Europe.
Villas-Boas sparked fears over his future last week as he claimed the Spurs superstar could leave the club this summer if they failed to make the top four.
But the Spurs boss back-tracked on Thursday, stating his comments had been misunderstood, and said he would be surprised if the 23-year-old left White Hart Lane.
Villas-Boas said: "The information that I have from the club, which was mistakenly written about last week, is that the player is here to remain, independent of the objectives of Champions League qualification being achieved or not.
"I would be extremely surprised (if he left).
"In football anything can happen. It's impossible to predict, but this is the assurance I have had from the club.
"We understand that the more awards the more recognition the player will have, the more media attention, but the club has to move forward by holding onto its best players.
"With the recognition and the further experience that he has had from this year, next year for Tottenham he will be even more assertive."
Bale's progress this year has not gone unnoticed by Real Madrid, but Villas-Boas and chairman Daniel Levy are digging their heels in over the player's future.
Villas-Boas added: "Whatever price tag the player has doesn't matter to us because he's our player.
"He's a player we have to hold onto for the remaining seasons to make sure that we reach our objectives and continue to progress as a club."
The Real hierarchy have always publicly remained coy on the prospect of adding Bale to their squad, but their sporting director Zinedine Zidane heaped praise on the Welshman this week, leading to speculation that a big-money bid could be on the cards.
Such words from a man of Zidane's standing will no doubt have caught Bale's eye, but Villas-Boas has no issue with the Frenchman's comments.
"It's fine, I have no problems with it," Villas-Boas said. "In the end it's great for a player of Zidane's dimension to be speaking about Gareth.
"It's good to have that public recognition from someone who has reached the biggest heights of the game."
Tottenham will need to have Bale on top form on Saturday if they are to register a much-needed win against his former team Southampton.
Spurs once held a seven-point lead over Arsenal, but a poor run of form means the Londoners sit two points outside the top four with four matches left.
They will need to beat the Saints to keep the pressure on Arsenal and Chelsea ahead of their crunch clash with the Blues next Wednesday, but Villas-Boas sees no reason to panic.
He said: "Nobody's shooting themselves in the foot. We are in an extremely good position, we have to our job to make sure we are successful.
"It's extremely competitive. To have 62 points at this point is extremely good."
Villas-Boas has the comfort of knowing that playmaker Mousa Dembele is likely to be fit after recovering from a muscle injury that forced him off in the first half of last week's draw at Wigan.
"He's making a good recovery, hopefully he joins training tomorrow and we'll reassess him and see how it looks. There is a good chance that he can play the game," Villas-Boas said.
Emmanuel Adebayor and Jake Livermore, who both missed the trip to the DW Stadium, are also available.