Discussions regarding a new deal for the midfielder have dragged on for some time, with there still no end in sight.
His failure to agree fresh terms has sparked speculation that the World Cup winner could soon be on his way to pastures new, bringing to an end his 12-year association with his boyhood idols.
City and Premier League rivals Chelsea have been heavily linked with moves for the 28-year-old in the past and would be expected to make a move should De Rossi become available.
Roma are reluctant to part with their homegrown hero, though, and the club's chief executive, Claudio Fenucci, is optimistic regarding their chances of reaching a contractual compromise.
"The operation is complex," he told Il Romanista.
"I don't think he has assessed any other proposals and is considering the option to renew his contract with Roma on top terms.
"Negotiations are ongoing, we are talking with his agent and will meet again soon.
"We are trying to fix all of the details and are looking for a solution. We are making every possible effort given the resources available.
"My perception is that we will reach an agreement. Because of the love that De Rossi has for Roma, I am sure he will not sign with anyone else until he has explored all options to extend his contract here."