Bale's stellar performances this season have won him a clean sweep of the PFA and FWA Player of the Year awards and turned the heads of some of Europe's top clubs.
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"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," Villas-Boas told reporters.
"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."
Real Madrid have been linked with a high-profile move in the summer, but Villas-Boas insists that there is no sum of money that could convince Spurs to part with their star asset.
"Whatever price tag the player has doesn't matter to us because he's our player," he continued.
"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."
Madrid's sporting director Zinedine Zidane recently praised the PFA Player and Young Player of the Year, claiming that he is the "best player in Europe this season", leading some to suggest that he was paving the way for a move to the Bernabeu.
However, Villas-Boas was unfazed by such comments, merely suggesting that the Welshman should be flattered by compliments from the France legend.
"It's fine, I have no problems with it," he concluded. "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."