With the German club enduring a frustrating season under former England manager Steve McClaren, Dzeko could be on his way to Eastlands when the transfer window opens at the beginning of January.
Dzeko has established a reputation as one of Europe's leading marksmen during his time in Germany, scoring 10 times this season and taking his overall tally to 66 in 111 games for the club.
Dzeko, who was also top scorer in the Bundesliga last season, joined Wolfsburg from FK Teplice for 4m euros in 2007.
City manager Roberto Mancini has spoken of his admiration for Dzeko before, but the club have now stepped up their pursuit of a player they regard as an ideal replacement for Emmanuel Adebayor, who they will try to sell in January.
Wolfsburg general manager Dieter Hoeness has declined to comment, while club spokesman Gerd Voss told BBC Sport: "We will not speculate on this.
"The silly season has begun with the January window about to open. We had it in the summer with Dzeko and we have it now again but we will not comment."
Bayern Munich currently hold the Bundesliga transfer record with their 30m euros outlay on Mario Gomez from Stuttgart in 2009.
The 27m euros paid by Juventus for Werder Bremen's Diego in May 2009 is the highest fee received by a Bundesliga club from a team outside of Germany.
Diego lasted only a season in Serie A, returning to the Bundesliga with Wolfsburg, who paid 15.5m euros for the Brazilian international.
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