The 29-year-old was linked with a move to the Premier League, with City boss Roberto Mancini a known admirer.
However, De Rossi does not want to leave his boyhood club, having been at the Stadio Olimpico since he began his professional career in 2001.
"I'm staying," De Rossi said at a press conference. "I never asked to leave."
De Rossi signed a fresh five-year contract in February to quell speculation of a move but City were reported to have tested Roma's resolve with a substantial offer this summer.
"One club, the one you all know, made an enquiry. One or two others, but that was just talk," added the Italy international.
"What I can promise everyone is that the day I want to leave Roma - whether it is to win the Champions League or make more money - I will say so in public."