Emmanuel Adebayor's decision to go to the African Nations Cup has led to renewed speculation that Spurs have reignited their long-term interest in the 23-year-old Internacional player.
Damiao has continuously stressed he would be interested in a move to Europe, although his club are said to be holding out for a fee in excess of £20 million.
Adebayor's absence leaves Villas-Boas with just one recognised striker in Jermain Defoe, but the Tottenham manager said that does not mean Damiao is on his way to White Hart Lane.
"Leandro is a player we've always appreciated, that this club appreciated before I arrived, but it's extremely difficult that he's going to join Tottenham," the Portuguese manager told a press conference on Thursday afternoon.
"He's a player that is highly rated in the market, and it's unlikely that he will play for Tottenham."
Damiao has been a leading star for Internacional since he signed for the club in 2009 and last summer he was top scorer for the Brazil side in the London Olympics.
Damiao denied that there have been any firm bids lodged for the him, but when asked whether he could guarantee Internacional fans he would be playing for them in the upcoming season, the 23-year-old told Brazilian website Zero Hora: "I guarantee that, for now.
"There has been no proposal, no negotiations. I am only thinking about Internacional. The president is the one who decides."
Internacional, who signed the striker four years ago, appear to be playing hardball in their attempt to keep hold of the hitman, with club president Giovanni Luigi reported to have said that only a "spectacular" offer will tempt him to part ways with the striker who was top scorer at London 2012.
Adebayor, meanwhile, has finally decided to play in the African Nations Cup.
After weeks of indecision, the 28-year-old has agreed to play in the tournament, which runs between January 19 and February 10, after receiving assurances from Togo president Faure Gnassingbe about team security at the tournament.
"I have met the head of state on two occasions. We talked, I told him what was wrong with Togolese football," said Adebayor, who was on the Togo team bus that was ambushed by armed gunman at the 2010 tournament in Angola.
"He must, at all costs, find solutions. We discussed it and he guaranteed that he will take charge of everything.
"In 2010 I wanted to go to the African Nations Cup to win and you saw all that happened, how that turned out. I hope this time will be better for me, for my team-mates, for all of Togo."