The 32-year-old defender has fallen down the pecking order at the Stadio Olimpico this season, with Mehdi Benatia and Leandro Castan preferred in the centre of defence.
Burdisso has made just six appearances for Rudi Garcia's side so far in 2013-14 and the Argentina international is keen to exit the club as he seeks first-team football ahead of the World Cup in June.
Genoa have been linked with a move for the former Inter man, who joined Roma permanently in 2010 following a successful loan spell with the capital club.
And Burdisso confirmed that he will remain at a European club, rather than returning to South America.
"I have decided to leave Roma," he told Sky Sport Italia. "I want to go to the World Cup in Brazil and I need to play more regularly.
"I won't go back to South America, I'll stay in Europe for the foreseeable future."
