The Blues failed with several bids for the Croatian over the summer which their final offer reaching up to £40 million according to Spurs boss Harry Redknapp.
It now appears Chelsea have given up on trying to lure the playmaker to Stamford Bridge as they will now look to pursue other targets.
When asked in a press conference about the possibility of another bid for the Croatian, Villas-Boas replied: "No I don't think so. The market is closed and I won't speculate what happens in January."
The Portuguese also admitted the Blues failed in a bid to sign full-back Alvaro Pereira from Porto as the two clubs failed to agree a fee for the Uruguayan.
He said: "We were very far from meeting Porto's demands for Alvaro. I am happy with Ashley Cole and Ryan Bertrand."
Meanwhile, Didier Drogba is slowly recovering from a concussion sustained in Chelsea’s 3-1 victory over Norwich.
Villas-Boas believes the Ivorian has a chance of making the Blues' clash with Manchester United on September 18 but has ruled him out of the side's first Champions League fixture against Bayer Leverkusen.
“He has to be authorised medically to make his full return to training,” Villas-Boas said.
“He has been doing light sessions, of course, with our physios.
“Let’s push it to the limit to try for him to be available for Man United.
“I wouldn’t say he would be available for Leverkusen.”
Villas-Boas added: “The first days were, of course, tremendous pain, and he had his family supporting him.
“He had complete support from the medical staff, who were with him 24/7.
“And we’ve been getting this support to him.
“We just have to make sure that he’s fully recovered before he comes back to training because that’s the requirement you have to do neurologically.”
The Portuguese tactician has been boosted by the news the goalkeeper Petr Cech will return to action at the weekend against Sunderland after being ruled out since the first game of the season.
David Luiz is also in contention to play at the Stadium of Light after missing the first three games of the campaign.
He said: "They are available for selection.
"David Luiz went with the national team [Brazil] last week. He was selected but not available to play because we felt he was in the last process of recovery. Both players have done extremely well since the whole squad got together yesterday."