Tottenham boss Harry Redknapp on Wednesday admitted it might be in his side's interests to sell the Croatia playmaker and spend the fee on strengthening their squad.
Chelsea have this summer seen bids of ?22million and ?27million rejected for the 25-year-old, who Spurs chairman Daniel Levy continues to maintain is not available at any price.
That resolve would undoubtedly be tested by a mega-money offer but Blues boss Villas-Boas has suggested there was a limit to what his club were prepared to spend.
Chelsea have been linked with a ?30million bid before the transfer window closes and Villas-Boas said: "We have approached Tottenham before regarding the player.
"I don't know if it's viable or not and to what extent we can go regarding his price because we are speaking about a high amount and nothing else basically. End of story.
"Whatever comes from Harry's mind is his own opinion about the situation.
"I just have to study the rest of the market and hopefully find a solution for my team."
Villas-Boas last week revealed he was attempting to sign two midfielders before the August 31 deadline.
As well as Modric, he has been linked with Valencia's Juan Mata, Liverpool's Raul Meireles, Porto's Joao Moutinho and the latter's wing-back team-mate Alvaro Pereira.
"That's a lot!" Villas-Boas quipped.
"Why don't we dwell on the names that already have been spoken about and never came?
"Neymar, (Samir) Nasri - how many names have been linked with Chelsea in the past and they didn't come?
"In our operations, in whatever we do or not in the market, we try to keep it as silent as possible."
He added: "We have been studying all kinds of options."
An injury to Michael Essien is a factor behind Chelsea's pursuit of a pair of midfielders.
Essien was last month ruled out until January after undergoing knee surgery, although Villas-Boas today revealed he was hopeful the Ghana star would be back sooner.
The new Chelsea boss suffered another injury blow on Wednesday when a training-ground accident saw goalkeeper Petr Cech ruled out for up to four weeks with medial ligament damage.
"It was the end of training, normal training incident," said Villas-Boas.
"He fell awkwardly with his weight on top of him and he stretched a little bit the medial ligament.
"We expected much worse when we saw the incident."
Villas-Boas must now decide whether to start Hilario or Ross Turnbull in Saturday's Premier League game against West Brom.
"Tomorrow, I think we'll make a full decision," he said.
Chelsea will be boosted by the return to full fitness of Branislav Ivanovic, who was an unused substitute in Sunday's opening-day draw at Stoke, but David Luiz (thigh) remains out until next week and Daniel Sturridge is still suspended.
New signing Oriol Romeu trained with his team-mates for the first time today after Spain's Under-20 World Cup exit but he will not be considered for selection until the Norwich game a week on Saturday.
Fellow new boy Romelu Lukaku, however, is finally available after completing his protracted move from Anderlecht today.
The 18-year-old Belgium sensation's arrival swells Chelsea's phalanx of strikers to seven and it is doubtful the club can keep them all happy.
There were reports this week that Nicolas Anelka wanted out after failing to start at Stoke, but Villas-Boas said today: "It's not true."
Yet, there is no sign of the Frenchman being offered a new contract to replace the one that expires next summer - unlike Didier Drogba, who is still in negotiations over an extension.
Asked what would happen if the parties failed to reach an agreement, Villas-Boas said: "We will [reach an agreement].
"He is one of the most important players and representative players of the club.
"And his willingness to continue is 100%. It will be because of that that we will reach an agreement."
Source: Team Talk
Source: Team Talk