Spanish giants Real are understood to have to lodged a formal bid of 60 million for the 24 year-old, with reports in Spain suggesting that the player is determined to move to the Bernabeu as a result of alleged 'broken promises' by Spurs chairman Daniel Levy.
Bale sat out Tottenham's 6-0 victory against South China in the Barclays Asia Trophy due to a muscle strain injury that also forced him to miss the midweek defeat against Sunderland in the same tournament.
And when asked after the game to clarify the situation about the Wales international, and whether a bid had been received, Villas-Boas repeatedly failed to shed light on the player's future.
"I don't want to comment on anything like that," the Tottenham manager said. "I cannot speak about anything."
When asked whether Bale had asked to leave the club, Villa-Boas added: "I cannot speak about this."
Although Manchester United are also keen to sign Bale, with manager David Moyes willing to compete with Real for the player, Real are understood to be the player's favoured option should he leave Tottenham.
Bale, meanwhile, is due to return to full training on Wednesday and could figure in Tottenham's friendly against Monaco next Saturday.