The Daily Star says City have offered De Rossi a bank-busting £160,000-a-week deal in a bid to lure him to the Etihad Stadium.
Boss Roberto Mancini is a huge admirer of the Italian and wants to land him in the January window as his next big-name signing at the Premier League leaders.
De Rossi, 28, is out of contract at Roma in the summer after failing to agree a new deal. The Italian international has spent all his career at Roma after joining his hometown club as a teenager and is reluctant to leave.
But Mancini is hoping to tempt De Rossi with a long-term deal worth more than £7m-a-season that would make him one of his highest-paid stars.