Spurs rebel Modric has been training alone since being fined last month for going AWOL in an apparent attempt to force through a move to Real Madrid. But new Tottenham boss Villas-Boas has warned the 26-year-old playmaker to be ready to accept he may end up staying and urged him to respond accordingly.
"He is training alone because we decided to do that until his mental state is ready to return to the team," Villas-Boas said. "It is important that, in the coming days, he understands he must return to the first team. We respect the player's ambition, but he must also respect the club."
Tottenham had been demanding £40 million for Modric, with Real having fallen well short of that valuation.
Paris St Germain have reportedly pulled out of the race to sign the Croatia star, who is at the centre of one of the transfer sagas of the summer for a second straight year after being denied a move to Chelsea 12 months ago.
Villas-Boas told reporters: "Until we receive a suitable offer for the player, he will not go. The contacts we have had with other clubs have not met with what Tottenham wants for the player. We respect the size of Madrid and the other interested clubs, but they must respect what we are doing too."
Selling Modric would have a huge impact on Villas-Boas's ability to bring in new signings, especially a top striker.
Tottenham have been heavily linked with Brazil's Leandro Damiao but the player's club, Internacional, are demanding a huge transfer fee of their own.
President Giovanni Luigi told O Jogo: "I think it's very hard for the transfer to happen unless Tottenham pay the 60 million euros (£47m) buyout fee that is included in his contract. Leandro Damiao has four more years on his contract. He is a very well-paid player and has nothing to complain about.
"And we don't need to sell. We are a rich club with an enviable structure."