The Italy international is one of several strikers to be linked with Spurs as Andre Villas-Boas weighs up his summer options.
The north London club, with just Jermain Defoe and Emmanuel Adebayor, are short of senior strikers, and Osvaldo is thought to be high on their list of potential transfer targets.
But Osvaldo's long-time friend and former-agent Dario Decoud doesn't think a move for his old client is likely.
"Osvaldo is very focused and wants to finish this season well," Decoud told Sport Mediaset. "Pablo wants to repay the faith show in him by [coach Auerlio] Andreazzoli.
"I know for certain that Roma consider him a key player and virtually non-transferable."
The Argentine-born Italy forward has six caps for his country, including his latest against Brazil this week.
The 27-year-old returned to Serie 'A' after a short, but successful, loan stint in La Liga with Espanyol.
Spurs are thought to have made a new striker a priority for next season. The club are pushing for a Champions League place, and Villas-Boas wants to build on his squad heading into the new season.
Adebayor was brought in last summer after a loan spell at White Hart Lane, but he's struggled to find the net. Gareth Bale is the club's top scorer with 21 in all competitions, while Jermain Defoe has 14, and Clint Dempsey has eight.