The highly-rated 22-year-old hinted on Tuesday that he was ready for a new challenge, but added any move hinged on his Brazilian club Internacional.
"I can't say much, it depends on Internacional too," Damiao said.
"Of course my wish is to stay, but there comes a time when you need to go. I don't know whether it is that time. If an offer arrives, then we will decide."
Tottenham manager Harry Redknapp reportedly sent the club's top talent scout Ian Broomfield to watch Damiao in Internacional's Brazilian first division clash with Coritiba on Sunday night, reported Xinhua.
The London club is understood to be willing to pay $24 million for the forward.
Internacional coach Dorival Junior admitted the club was prepared for the prospect of losing the star striker.
"We have to get ready," Dorival said. "There is nothing concrete yet but it is natural that several players draw attention.
"We will try to anticipate any loss by signing another player to minimize any damage to the team."
Damiao has scored 18 goals from 25 first-team appearances for Internacional in 2012.
He has also reportedly attracted interest from Porto, Arsenal, Liverpool and Juventus.
Leandro Damiao poised for Tottenham move
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