Tottenham boss Harry Redknapp admitted it might be in his side's interests to sell the Croatia playmaker and spend the fee on strengthening their squad.
In demand: Chelsea are interested in Tottenham midfielder Luka Modric
Chelsea have this summer seen bids of ?22million and ?27m 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 ?30m bid before the transfer window closes and Villas-Boas said: 'We have approached Tottenham before regarding the player.
In charge: Villas-Boas was coy over the future of Modric
'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.
Blow: Cech has been ruled out for four weeks
'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.'
The new Chelsea boss suffered another injury blow yesterday 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.'
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Source: Daily Mail
Source: Daily Mail