Spurs are reported admirers of the Brazilian striker, who currently plies his trade with Internacional.
Discussing the 22-year-old's future, agent Vinicius Prates has revealed that Harry Redknapp firmed up his interest in the centre-forward by making an unsuccessful offer at the turn of the year.
"The only concrete offers in January were from Tottenham and PSG," agent Prates told Calciomercato.com. "There is a good chance that the player will arrive in Europe this summer and it would be a good opportunity for him to play at a big club."
Damiao has 21 league goals in 53 outings for Internacional.