The giant forward has attracted the attention of most major clubs in Europe but it seems Manchester City are closing in on Dzeko, having agreed a fee with Wolfsburg that is believed to be around ¦pound;27million.
"We have agreed a fee with Wolfsburg and I am confident he will come but we must wait," said the City chief.
Personal terms have still to be sorted, as has a work permit, although that will be automatically granted as the 24-year-old has won 31 caps since making his international debut in 2007.
And with no Premier League game until January 15 after Wednesday night's trip to Arsenal, City see no requirement to rush the transfer through.
But when the player - top scorer in the Bundesliga last season - does eventually arrive at Eastlands, Mancini knows he will be getting a high-quality performer.
"We have an important game, so we must keep our focus on it," he added. "But all the teams in Europe want Dzeko, which is a sign that he is a good player."
Mancini feels Dzeko's power will compliment the greater finesse of skipper Carlos Tevez and Mario Balotelli, who, along with David Silva, has been ruled out of the crucial Emirates Stadium clash with a knee injury.
It should also herald the departures of Emmanuel Adebayor and Roque Santa Cruz, although City officials have stated that, as yet, there are no deals on the verge of being concluded, the same also being true of Wayne Bridge.
Although City did receive a request from West Ham to take Bridge on loan, the Londoners were apparently willing to cover a portion of the former England full-back's ¦pound;80,000-a-week salary, and the Blues were unwilling to make up the difference.