Modric's refusal to travel to USA has infuriated Spurs, as Goal.com revealed on Monday that the Croatian's decision has made chairman Daniel Levy more determined than ever to hold out for his £40 million asking price or force his star to stay rather than be bullied by the player.
Villas-Boas told reporters: "There are clubs interested in him but we have to hold on to our values and our rights and at the moment the situation for Luka is he is under club discipline.
"Unfortunately for him he's going to have to be fined for not being present.
"He's a player who has offered so much for Tottenham so we have a sense of respect for what he's done over the years for us but the chairman feels that the fact that he's not present is not common professional behaviour.
"The situation can be solved in two ways, the two ways being that the clubs interested meet the demands of Tottenham regarding the player's value or the player continues and returns to the club.
"Hopefully this is a situation that won't drag on for long. The situation is not dependent on Tottenham, it's dependent on the clubs who are interested in the player.
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"This type of player revolt is not new but I think that clubs have to protect themselves. There's plenty of time in the market.
"It's the first time unfortunately for Luka that he takes these actions. I think the chairman and myself have been very open by saying we are willing to listen to offers for the player, which is uncommon, I think.
"He's had many interests in the past like last year but he has always behaved professionally. We never doubted his human qualities so we don't know what kind of advice he's receiving."
Modric did finally turn up for training with Tottenham on Monday, as revealed by the club in a statement on their official website: "The club can confirm Luka Modric has returned to training today [Monday] at Spurs Lodge.
"The coaching staff will now determine the remainder of his pre-season preparation."