After resisting pressure from City last season, De Rossi is set to perform a dramatic U-turn and accept a €9 million-a-year deal to move to England.
Mediaset says a chat with City manager Roberto Mancini convinced De Rossi to change his mind.
"Do you want to end up like Totti?" quizzed Mancini. "A great player, who has never won anything?"
City hope to do business with Roma this week for around €30 million.