Spurs have been on the trail of the Internacional striker for some time, with a January swoop for his services collapsing on deadline day.
Andre Villas-Boas has continued to monitor the 23-year-old since then, with a second approach this summer believed to be in the pipeline.
Spurs are, however, not the only side in the running for Damiao's signature, with Italian outfit Napoli having joined them at the head of the transfer queue.
Damiao's representative is refusing to close the door on any possible deal as the window of opportunity prepares to swing open once more, and he insists Tottenham remain an attractive option for his client.
Vinicius Prates said: "Of course all players dream of playing in the Premier League.
"Tottenham are an important club in London, we can't rule them out."