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."
Wolfsburg's managing director Dieter Hoeness declared last week that his club is preparing to make major changes to the playing personnel after a disappointing first half of the season.
Selling a player of Dzeko's talent may not be his preference, but the player's malaise at the 2009 Bundesliga champions, who currently seem unlikely to provide him with the chance to play in the Champions League next season, may be one of the reasons the team has not been functioning since Steve McClaren took over as coach in the summer.
A fee of 40 million euros, which the Wolfsburger Allgemeine reports would be made up of an initial fee of 30 million euros with five million to follow in the case of City qualifying for the Champions League, while five million euros would go on signing-on and agent fees, would break the Bundesliga's transfer record.
The Wolves are set to make a huge profit on a player they signed for just four million from FK Teplice in 2007.
Dzeko has already found the back of the net 10 times this season, taking his overall tally to 66 in 111 games for the Wolves.