Emmanuel Adebayor's decision to go to the Africa Cup of Nations with Togo prompted speculation that Spurs would step up their bid for the 23-year-old Internacional player.
But though Adebayor's absence leaves Villas-Boas with just one recognised striker in Jermain Defoe, the Tottenham manager cooled expectation of an imminent arrival.
"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," Villas-Boas said.
"He's a player that is highly rated in the market, and it's unlikely that he will play for Tottenham."
Damiao, rated at £20m, has impressed since joining Internacional in 2009 and was Brazil's top scorer at the London Olympics.