De Rossi, 29, who has been a target for City for the last 18 months, signed a new five-year contract with his club in February.
That is sure to make it harder for City to lure him away from the Italian capital, but they undoubtedly have the cash to do so, The Daily Mail reports.
City has so far been quiet in the transfer market this summer, although Mancini is keen to add more strength and depth to his side as they bid to defend their Premier League title in the coming season.
De Rossi is a product of the Roma youth system and has spent his entire career with the club from the Italian capital, playing nearly 300 games and winning the Coppa Italia twice in the process.
De Rossi was also part of the Italy side that won the World Cup in 2006, scoring in the penalty shootout. (ANI )