The Bosnian striker has made no secret of his desire to leave the German side for a bigger club and, while his dream has always been to join AC Milan, the fact the Italians have just signed Antonio Cassano from Sampdoria reduces the chances of that move coming off.
However, City have the ambition to become one of Europe's top clubs and they also have the financial backing, and a transfer of Dzeko next month is looking more likely.
Coach Roberto Mancini has also confirmed that he is a fan of the 24-year-old.
The Wolfsburger Allgemeine newspaper quotes Mancini saying: "We have the chance to win the league this year and the decisive factor could be Edin Dzeko. This player can decide titles and that is why we want him."