The Daily Star says City are closing in on £25m Italian World Cup winner De Rossi.
City have been trying for months to sign De Rossi, who turned down a move to the Etihad last summer.
Roma general manager Franco Baldini said earlier this month: “Manchester City made an offer for De Rossi during the summer. We listened to the offer, and considered it.
“If we were to get another offer from them we would listen again.”
Chelsea also showed interest in De Rossi before Roberto Di Matteo’s sacking as manager last week.