The Wales international was expected to meet up with his Spurs team-mates but he did not turn up and is unhappy with how the club are dealing with the situation, Sky sources understand.
Bale has always reported to the Hertfordshire base for treatment on his supposed foot injury ever since it stopped him from playing for the north London club.
But the forward did not turn up on Tuesday and no explanation has been given as to why.
A Spurs source said there was "no issue" with Bale not turning up, and insisted that the player remained in touch with Villas-Boas about his training regime.
And Bale's camp tried to play down the suggestion that the triple player of the year had become "furious and frustrated" with Tottenham's handling of his proposed transfer to Madrid.
Tottenham insist they will not sell Bale to Madrid until they have signed at least one more player to replace him.
Talks in London are ongoing with Roma over the possible transfer of midfielder Erik Lamela, but Villas-Boas' hopes of being reunited with Zenit St Petersburg forward Hulk look set to be dashed after the club's manager Luciano Spalletti said the Brazilian was not for sale.
Real's hand has been weakened over the course of the last week thanks to their antics.
Villas-Boas was annoyed with Real after they made their pursuit of the player public, and it is understood that Daniel Levy has become further dismayed with the Spanish club over the last few days.
The Spurs chairman has not taken kindly to the idea that Real started selling replica shirts with Bale's name on the back, and their decision to erect a stand at the Bernabeu from which they planned to unveil their latest Galactico.
Although Bale has his heart set on a move to Real, it emerged on Monday that Tottenham are considering at least one more offer for the player.
Manchester United have enquired about Bale's availability in the past, but manager David Moyes denied they had renewed their interest in the player.
Asked if United had made a bid, he said: "No."
But having not yet made a major signing since taking over at United, Moyes cryptically mentioned that he was still on the lookout for new players.
He said: "I have just said Manchester United are always interested in the best players.
"The board and myself would always be looking to sign who we think are the best players, whoever they are."
Bale spent the weekend in Marbella after Villas-Boas gave him the weekend off and the forward is now expected to miss the club's Europa League clash against Dinamo Tbilisi on Thursday night.
Spurs icon Glenn Hoddle has claimed Levy still harbours hopes of holding on to Bale, who scored 31 goals for club and country last season.
"I was at the Swansea game at the weekend and had a good chat with Daniel Levy," Hoddle told talkSPORT.
"He's ambitious and believes, if Bale was to stay, that Tottenham could go on and do something really strong in the Premier League."
Hoddle, who played at Spurs for 12 years before later going on to manage the club, thinks Levy will want to bring in more players soon after missing out on Brazil international Willian, who chose Chelsea over Tottenham last week.
"It's difficult for Daniel Levy to stop a player joining Real Madrid," Hoddle added.
"When they come knocking, and the lad wants to go, it's difficult to say no.
"I get the feeling there's more business to be done though. Levy wants to strengthen the squad.
"They needed Willian but he's gone to Chelsea, and he must get someone who can unlock the door.
"I've never seen a Spurs side look so powerful physically but they need someone, dare I say it like Gareth Bale, who can change the game.
"Now, if they are preparing for life without Bale, then they definitely need to go into the market and buy a replacement who can open the door, but you can't pick that sort of player up easily."