Welshman Bale was named Footballer of the Year by England's soccer writers on Thursday after being picking up the PFA Young Player and Player of the Year last weekend and he is regularly linked with Europe's top clubs.
Tottenham's determination to keep a player who has scored 24 goals in all competitions this season will be severely tested if they fail in their bid for Champions League qualification, but Villas-Boas says he has received assurances that the winger's future is not dependent on a top-four finish.
"The information I have from the club that was mistakenly written about last week is that the player will remain here irrespective of Champions League qualification being achieved or not," Villas-Boas told reporters at Tottenham's training ground on Thursday.
"This is the information I shared with you all of the season. The more rewards, the more recognition the player has, the more media attention, but this club can only move forward by keeping hold of its players and next season for Tottenham, Gareth can be even more assertive.
"I would be extremely surprised [if he left this summer], but in football anything can happen. It is impossible to predict. This is the assurance I have from the club."
"Whatever the price tag the player has doesn't matter to us because he is our player," added Villas-Boas.
"He's a player we have to keep hold of for the remaining seasons to make sure we are to achieve our objectives."
Tottenham are just outside the Champions League qualification spots in fifth place with 62 points but would nail down a top-four finish if they won their remaining four games.
They face Southampton on Saturday when victory would temporarily lift them above fourth-placed Arsenal.
Next Wednesday's clash with third-placed Chelsea, who they trail by three points, could be decisive.
"I firmly believe points will be dropped by all the teams involved," Villas-Boas said.
"It will be extremely difficult to win all four games because we have Chelsea away but that's our ultimate objective.
"We have 62 points and eight adrift from 70 which was the objective when we set out and it's perfectly achievable with 12 points still to play for."
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