Internacional have been insistent that they have not fielded any offers for the 23-year-old, but his agent Jorge Machado has claimed talks are ongoing with an unnamed club.
Tottenham have been long-term admirers of the striker and have made more than one offer in the past 18 months, but now reports suggest it is another Premier League club in the shape of Southampton that is pushing strongest for him.
"There is a club interested [in Leandro]," Machado told UOL.
"We have been talking with Internacional for many days, but we have to wait.
"Inter have set a value, which is very significant, so we need to have more talks."
Internacional's director of football Luis Cesar de Souto Moura reiterated the club's position.
"There is no offer for Leandro Damiao," he told Radio Guaiba.
"We understand the following as an offer: when an agent or club make an official enquiry and expresses interest in the player."
He also added that the club would want over £20million for the player.
"An offer for Leandro Damiao will only be considered if it's around €25 million," emphasised Moura.