It will take £40 million ($60 million) to prise
Tottenham is willing to sell Modric at the right price but PA Sport understands it is looking for a fee nearer to £40 million than the widely-reported figure of £35 million.
Manchester United and
"There has been continuous interest in Luka from three clubs in Luka," the Portuguese said.
"But it is important for Tottenham to hold on to their rights. His situation will continue as it is until the price is right.
"It's important to understand his feelings. We have been speaking and I understand his point and he understands the club's point."
Modric first stated his desire to leave the north Londoners last northern summer after the team failed to qualify for the UEFA Champions League.
Tottenham stood firm, but speculation has been rife again recently after Chelsea's triumph in this year's Champions League final meant Spurs once again missed out on
"Luka is an intelligent person and understands the club has to defend its values, rights and interests," Villas-Boas added.
"It's a difficult situation for the club but we have been co-operative by openly saying we are willing to listen to offers.
"But the offer has not been met to what the chairman [
Spurs head off on their pre-season tour to
It is understood Tottenham are unlikely to make any more signings before jetting off, although a deal for Manchester City's Emmanuel Adebayor continues to be negotiated.
Lyon goalkeeper Hugo Lloris is another reported target for Villas-Boas, who was the subject of apparent criticism from Porto's Danilo.
The Brazilian defender supposedly posted on Facebook his disappointment at the Tottenham boss for meeting his club-mate Hulk at the Olympic team's hotel.
However, Danilo has quickly moved to clear up the situation and denied making the comments on former Porto boss Villas-Boas.
"Various Portuguese media reported something I supposedly said, criticising the visit of former FC Porto technician
"I admire the work of the Villas-Boas and do not see any problem in paying a visit to a friend with whom he worked and was very successful! #clarification"
English Premier League
West Ham United has completed its first transfer of the post-season after signing Romania international fullback Razvan Rat on a free transfer.