The 24-year-old, whose prolific scoring record in the Bundesliga has seen him emerge as one of Europe's most sought-after players, will command a fee in the region of 30 million pounds, according to British media reports.
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"We have an important game at Arsenal coming up and I will speak about him after that," Mancini told a news conference.
"We've agreed with Wolfsburg. He's a good player and all the teams in Europe want him."
Abu Dhabi-owned City, who are currently second in the Premier League behind Manchester United, have already invested heavily in attacking talent but have come to rely on the goals of Carlos Tevez.
Emmanuel Adebayor, Roque Santa Cruz and Mario Balotelli have all failed to establish themselves as regular striking partners for the Argentine despite arriving for inflated transfer fees.
Dzeko finished top of the Bundesliga scoring charts last season with 22 goals and already has 10 to his name this campaign despite featuring for a side struggling in mid-table.
Wolfsburg boss Steve McClaren said recently it would be a wrench to let Dzeko leave but City would be recruiting an "ideal" player.
"He is a good buy for them," he told the Daily Telegraph. "He's a good boy but he needs to work harder now he is in the Premier League than he does at present. But he will adjust, no problem."
