Aston Villa manager Martin O’Neill announced on Thursday that Milner had informed the club of his desire to quit Villa Park for Eastlands.
O’Neill is prepared to let the 24-year-old leave, as long as City match the club’s value of the player, believed to be in excess of £25 million.
Mancini, who has already signed Yaya Toure and David Silva this summer to boost his midfield options, is hopeful that the two clubs can reach an agreement.
“Milner is a good player, but today he is an Aston Villa player," Mancini told Sky Sports News.
"If we have this chance [to sign Milner] I think we can take him, but we must wait now."
City goalkeeper Shay Given also praised Milner’s abilities while also acknowledging the quality the Blues already boast in that position.
"I worked with James at Newcastle and he is a very, very good player, but we have got some great players already," Given said.
Veteran French midfielder Patrick Vieira, who is one of 13 first team midfielders City currently have on their books, was also pleased to hear that the current PFA Young Player of The Year could soon be joining Manchester City.
"He [Milner] is a terrific player," said Vieira. "Of course it is not my place to say if he has to come or not but when you look at players we have around it will be good.
"The attraction of City is that the future is fantastic. We have a really competitive team and I think every single player will want to play for City because the future is bright for City."
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