De Rossi, 29, had been targeted by City manager Roberto Mancini and held a press conference on Tuesday to explain his position.
The Italy midfielder, who was born in Rome and has only represented Roma during his career, said he had no intention of joining the Premier League champions.
"I have decided to stay," De Rossi said. "I never asked to go to Manchester City.
"One club, the one you all know, made an enquiry. One or two others, but that was just talk.
"I promise that the day I do want to leave, I will hold a press conference and tell you."