Spurs are reported to have been tracking the Brazil international for some time, with speculation regarding an official approach having intensified since the transfer window re-opened.
Andre Villas-Boas is in the market for attacking talent, with the news that Emmanuel Adebayor is to join up with Togo for the Africa Cup of Nations set to leave Spurs with just one senior frontman in Jermain Defoe.
Damiao would represent something of a gamble, with the 23-year-old untested in Europe and set to demand a sizeable fee.
He is also in no rush to leave his homeland, despite claims by Internacional president Giovanni Luigi on Wednesday that a bid has been tabled by an English club.
Damiao claims to be unaware of such an approach and maintains that his focus is locked on the forthcoming campaign with Internacional.
He told Zero Hora: "My agent told me that there is no offer, everyone around me knows that I want to stay.
"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".