The Blues have been chasing the FK Partisan defender since the end of the 2010/11 campaign, with his obvious potential drawing admiring glances from across Europe.
At just 20 years of age, the Montenegro international is regarded as a hot prospect for the future and a number of sides have expressed an interest in acquiring his services.
City, though, appear to have edged out their rivals in that particular pursuit, with an agreement to bring him to Eastlands almost sealed.
Mancini has confirmed that Savic is close to completing a move, while he has also admitted to being in the running to land Arsenal midfielder Samir Nasri.
He said: "I would say a deal for Savic has been done, but Nasri? No, not yet."
City's Italian coach has also speculated on further new arrivals at Eastlands, with a number of Serie A's leading lights catching his eye.
Mancini added: "I like Ezequiel Lavezzi, Marek Hamsik and Edinson Cavani.
"I like Javier Pastore a little less.
"When I think of Udinese, I can think of Pable Armero and Mauricio Isla.
"And I must say Antonio Di Natale. It's a pity that he is now getting on in years.
"I also liked Radja Nainggolan of Cagliari.
"Of course, I did not mention the Inter boys for whom I have a weakness. I think the ones I coached are great players."
Source: Team Talk
Source: Team Talk