Spurs boss Andre Villas-Boas has been keeping tabs on the 27-year-old Argentinian, who has bagged 12 goals so far this season for the Italian Serie A outfit.
And, despite Osvaldo having three years remaining on his contract at the Stadio Olimpico, it was suggested that a fall-out with club legend Francesco Totti would see him made available for transfer this summer.
But Spurs' hopes of luring the player to White Hart Lane look to have been shattered because Osvaldo's former agent and friend Dario Decoud is adamant that he is staying put.
"Osvaldo is very focused and wants to finish this season well," Decoud told Sport Mediaset.
"Pablo wants to repay the faith shown in him by [Coach Auerlio] Andreazzoli.
"I know for certainty that Roma consider him a key player and virtually non-transferable."