However, a transfer now looks unlikely after Internacional vice-president Luciano Davi stated that they want to keep the 23-year-old.
"Our intention is that Leandro Damiao doesn't leave this year," Davi told Globo Esporte.
"He is an Internacional player until December. Their offer wasn't relevant and we are not interested in selling him.
"Tottenham came to us but their offer didn't match our valuation of him. Leandro Damiao is a national team striker and we have to value that."
Spurs host Norwich City at White Hart Lane in their next Premier League match on Saturday.