The Italy striker has been linked with a move to AC Milan, among others, as of late, but he is hoping to remain with the Giallorossi for the foreseeable future.
The Italy international has been touted as a potential replacement for Alexandre Pato, who left AC Milan for Corinthians on Thursday, but the player is adamant that he will stay put.
"I hope that Roma are my future," Osvaldo told Sky Sport Italia. "I never said I wanted to leave Roma. I want to stay for a long time. [The club's hierarchy] only spoke to me to find out if I was okay."
Roma returns to action with a clash against Napoli on Sunday, and Osvaldo is hoping to do better than Edinson Cavani to help him climb up the scoring charts. Cavani has 13 goals compared to Osvaldo's nine, but both men are trailing AC Milan's Stephan El Shaarawy, who has 14 Serie A goals.
"The match against Napoli will be a great spectacle for the people. Cavani is better than me, but I think we can get there to move ahead of Napoli," Osvaldo said.