The Daily Star says De Rossi has been a long-time target for Manchester City, but the West London club are now thought to be ready to join the race.
The new interest coincides with De Rossi holding talks with club director Walter Sabatini to discuss his future at the club.
The club's American president James Pallotta recently revealed he would be willing to listen to offers, insisting no player was sacrosanct.
He told Italian television network RAI: "De Rossi? We’ll see. Everybody is on the market, just as they are for the Boston Celtics."