The Brazil international has been a long-term target of Spurs, who will be reduced to one recognized striker this month as Emmanuel Adebayor heads to the Africa Cup of Nations
After Saturday's Premier League fixture against QPR, Jermain Defoe will be Spurs' only recognized first-team striker as Emmanuel Adebayor will travel to South Africa to join Togo's Africa Cup of Nations squad, with the tournament ending on Feb. 10.
Damiao has been previously linked with a move to White Hart Lane, but the Tottenham manager insists the 23-year-old won't be brought in to bolster his attacking options during the January transfer window.
"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," said Villas-Boas.
"He's a player that is highly rated in the market, and it's unlikely that he will play for Tottenham."
Damiao has also reinforced his intention to stay at Internacional this month but the Brazil international concedes he could move clubs in the future.
"My agent told me that there is no offer, everyone around me knows that I want to stay," Damiao told Zero Hora.
"But I can't say that I'll stay forever, maybe there will be an offer in the long term and (my future) depends on the president too".