Bale recently admitted he would one day like to play abroad, and Madrid have been heavily linked with a move for the winger as they look to kickstart a campaign in which they sit third in the league, some 11 points behind Barcelona.
Although Bale recently signed a new contract, there is a fear his head could be turned if Real's players start to court the player in the same way Barcelona did with Cesc Fabregas in 2011.
Villas-Boas -- whose side play host to London rivals Fulham this afternoon -- admitted earlier this week that he expected interest in Bale after the Welshman's excellent form this season, but today made it clear that the winger is not for sale.
"Obviously Modric is aware of Gareth's performances because of his love for Tottenham and the fact he is very connected with him and this football club, but it's completely impossible (for Bale to leave)," the Tottenham manager said.
"We have to protect our assets regarding our objectives.
"We have to qualify for the Champions League so in order for that to happen we need players that can make the difference.
"We are not looking to sell."
Bale recently insisted he is happy at White Hart Lane and there is no suggestion he will try to force his way out in the same way that Modric did.
Revered by the club's fans for his exquisite displays during the first two years at Spurs, Modric angered the supporters by pushing for a transfer to Chelsea before doing the same the following year when Madrid came calling.
Villas-Boas, who ordered Modric to train on his own after he declared he wanted to move to Spain, made his annoyance clear at the midfielder's comments regarding Bale, adding: "He should focus more on his club than ours."