Andre Villas-Boas has made no secret of his desire to bring a forward to White Hart Lane during the summer and the Brazilian appears to be at the top of his wish list.
Marseille were also looking at acquiring the services of the 23-year-old but announced that they were unprepared to meet the asking price of £17million.
Spurs narrowly missed out on Champions League football this season, which could be a stumbling block if any other clubs come knocking for the man who netted 17 goals in 32 league games this term.
Marseille sporting director, Jose Anigo said: "Leandro Damiao? We know him very well, but there are financial aspects we cannot ignore. We are following him but it is too expensive so far. On a financial level we will be more at ease than last season, but we didn't win the lottery. Our priority is to try to sign French players."