The Brazil international is contracted to his club until 2015, but has been the subject of much speculation over a possible move to Europe.
Spurs manager Andre Villas-Boas is a known admirer of the 23-year-old striker, but the Nerazzurri are now also said to be showing an interest in the player who was the leading goal scorer at the 2012 Olympic football tournament.
An offer from Spurs was rejected by Internacional last summer, with the Brazilian club feeling Damiao had been undervalued.
Luigi has previously revealed that Damiao has a €60million (£47million) buyout clause in his contract, and has now rebuffed talk of a bid from Italy.
"Inter Milan interested in Leandro Damiao? Someone told me about it, but there were no direct contacts and we have never received a direct offer," Luigi said.
"This did happen with some clubs from the English Premier League.
"The future of the player? When we get an important offer, we will evaluate it. But to sell in January, this would have to be a very, very attractive offer."