Tottenham have reportedly had a bid of £10.6m turned down according to officials at Internacional.
The North London club currently lead the race for the Brazilian striker due to the commercial link between the two.
With Spurs heavily linked to moves for both Didier Drogba and Miroslav Klose in this mornings papers, their first action in the transfer window has been thwarted up front.
"It's the first offer we have received and we have refused it." club president Giovanni Luigi said.
"I said I didn't want to sell now. I warned that he'll only leave and the end of the year and for more money.
"Tottenham offered €12m for Damiao, but we think it is not enough for a player who is 21 years old and has an excellent future."
It remains to be seen whether Spurs will make a renewed bid for the striker, who has scored 22 goals in 24 games for Internacional.
Leandro is valued at £17m which sees Spurs offer fall way below that valuation.