Real Madrid have made it clear that they are keen to sign the Welshman and are believed to be willing to pay what would be a world record transfer fee.
However, Villas-Boas said after Saturday's friendly defeat to Monaco: "These rumours of an imminent transfer are not true.
"The only thing we have communicated with Real Madrid is that he is our player and he is not for sale."
Bale has not made yet made his feelings public but Sky Sports reporter Amy Lewis said: "I've been speaking to a source close to Gareth Bale, who says that Bale is both unhappy and disappointed by the comments his manager made in that interview. In particular, that he is not for sale.
"Gareth Bale missed the match with Monaco yesterday because of a foot injury and I've been told it's unlikely he'll take part in training next week.
"A lot has been said about how much Madrid would be willing to pay for Bale. I've simply been told it's a world record fee, so upwards of £80m.
"It's not clear whether Bale will put in a transfer request but the source is still pretty confident that the player will be moving to Real Madrid. Nothing is imminent though."