The Wales international has been in scintillating form this campaign, scoring 18 times in the Premier League to help fire his side into fifth in the table.
Goal.com exclusively revealed in March that Bale was prepared to reject a summer move if a place in Europe's premier competition was secured, while Manchester United were quoted a £70 million price tag when enquiring later the same month.
Tottenham are currently one point behind fourth-placed Chelsea with five games to go and when asked if he had been given guarantees over Bale’s future and whether he would stay if the club secured Champions League football, Villas-Boas told reporters: "I think so. That's the information that I have from the club. It has come from the club."
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"The club is committed to keeping the best assets. That's the only way that we can ensure that we are in the fop four every year," he added. "Gareth is part of that project bearing in mind that he has been amazing this season.
"Hopefully, we can develop him to a greater extent. We get the buzz from working with great players and Gareth has developed into a great player, so I couldn't be happier."
Bale is the favourite to be named the Professional Footballers' Association Player of the Year and Villas-Boas is hoping the winger can scoop the prize.
"Gareth has had a major development this year," he said. "He has played in so many positions and has had such a big impact in those positions. We are happy that he has been nominated [for the PFA award] and we would be even happier if he was to win.
"Although the recognition is individual, the team have helped him to have this wonderful year and they would feel good for Gareth. They are an excellent group and everything they have spoken about Gareth is with respect."