The City coach has endured a frustrating summer in the recruitment market and has only managed to sign midfielder Jack Rodwell from Everton for £12 million last week.
With rivals Manchester United and Chelsea spending heavily Mancini is desperate to add three first team players to his squad before the end of August.
Roma enforcer De Rossi is reportedly close to signing for the club with the 29-year-old Italy international open to a lucrative switch to the Etihad Stadium.
Mancini is hoping it will ignite a flurry of activity with rumours gathering that he is planning a fresh bid for Liverpool defender Daniel Agger with the club seeing it’s business stifled by FIFA’s new financial fair play regulations.
The former Inter Milan coach has desirers of reaching the levels achieved by Barcelona and Real Madrid but is aware that he needs to boost his numbers with a Champions League campaign on the horizon.
“I’m happy with Jack (Rodwell) because he is young and a really good player. But we need to have other players,’ said Mancini.
“When the Champions League starts, we will be playing every three days for 10 months. This is not easy if we don’t have players.
“We could also lose Yaya Toure when the Africa Cup of Nations is played in January.
“We will work hard to get players before the window closes in the next 10 days, but it will be difficult.”
A 3-2 win at home to newly promoted Southampton kicked off the defence of their Premier League title and City are hoping the appointment of new chief executive Ferran Soriano will smooth over relations between Mancini and Brian Marwood.