The north London outfit made a last-ditch attempt to sign Leandro Damiao in the January transfer window, but Internacional rejected the bid.
While Gareth Bale has been in free-scoring mode for Spurs, they need more firepower up front.
Under-fire forward Emmanuel Adebayor has been short on confidence and goals, and Spurs could up the ante for Osvaldo in the summer.
Osvaldo though is perceived a disruptive influence according to his former Bologna coach, Franco Colomba.
He was quoted on Italian football site Forza Italian Football, as saying: "Osvaldo has potential talent, but is always missing something, especially in terms of his character.
Andre Villas-Boas is weighing up his attacking options
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“Football is a team sport and that comes first, unless you are the kind of player who scores two goals per game.
“He wants to be a protagonist and when he’s on the bench he feels aversion towards his teammates.
"In a squad, even those on the bench are part of the game, but Osvaldo can’t stand that and pays the consequences."
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