The striker is one of the few top class strikers in the world today not residing in what would be regarded as a top club. However, the deal may not be as simple as a mere £25 million bid and buy.
It is no secret that Wolfsburg is having a poor season. Currently, Die Wölfe are languishing in 13th, a massive 24 points off Borussia Dortmund in first place and are facing a real struggle to stay in the league, never mind qualify for Europe or challenge for the title as many expected.
The signing of ex-England boss Steve McLaren from FC Twente was meant to be the catalyst that propelled the Volkswagen backed team towards becoming perennial title challengers, but the move has not worked as hoped.
Under McLaren, Wolfsburg got off to their worst start to a league campaign in recent memory with three defeats in their opening three games.
The situation improved somewhat after that though as Die Wölfe went unbeaten for four games with three straight wins.
However, things then took a slight turn for the worse and as we head into the winter break, Wolfsburg have gone eight games without recording a win and have suffered an embarrassing defeat to Energie Cottbus in the German Cup.
That shock defeat caused the Club President, Dieter Hoeness, to release a statement backing McLaren but also sending a shot across the bows of players with perceived bad attitudes.
Hoeness told the club's official website: "We have got some cleaning up to do.Hoeness intimated that McLaren had much work to do and that January would be an important month for getting the Wolfsburg project back on track.
"We told the team eight weeks ago after the defeat in Nurnberg that their basic attitude must change.
"We did not get a reaction so now we have got to react. The fans do not deserve to see what they are seeing on the pitch, particularly given the exemplary way in which they supported us against Cottbus.
"We expect the coaches to act consequentially and to punish bad behaviour both on and off the field."
"Above all, we will push on with our rebuilding of a successful team next summer," explained Hoeness.
"It is difficult to do that in the winter, but we will see what we can do.
"It is going to be a painful time for one or two people around here. With this current team in this current situation, enduring success is no longer possible."
Wolfsburg's sliding down the table has had a huge effect on the team, chiefly its talismanic goal scoring machine Edin Dzeko.
The striker has made no secret of his love for Die Wolfe, but he has also made it clear that he will move if he does not receive regular Champions League action.
At the start of December, Dzeko and McLaren had a heated exchange after the Bosnian striker was substituted with two minutes remaining in the 0-0 draw against Werder Bremen.
It was the first public sign that all was not rosy in the Wolfsburg garden and almost immediately, Europe's top clubs came circling.
Manchester City is believed to have placed a bid of around £25 million (€40m) with the club for Dzeko's services, but thus far the club have remained tight lipped.
The main problem Manchester City face in signing Dzeko is that Wolfsburg are probably the only other club in the world where money is not a major factor in sales.
The club grew out of Volkswagen wanting an outlet for their workers in the newly created city of Wolfsburg and the club have become something of a play thing rather than a business enterprise for the world famous car group.
In short, VFL Wolfsburg does not need to sell players to balance the books and are not run for profit.
It is also worth noting that Volkswagen owns Audi and that Audi own a 10 percent stake in Bayern Munich.
Over the last couple of seasons, there have been persistent rumours that Bayern Munich have first preference on Dzeko and it seems very surprising not to hear their name being mentioned as the bidding war for the Bosnian's services begin.
On top of the Bayern Munich links, you also have to look at Manchester City's bench. Brian Marwood was brought into the club with a view to reducing the club's wage bill with "Financial Fair Play" in mind and it was partially his doing that the club have dramatically reduced their reliance on using players’ agents.
Agents being moved to the periphery of importance at Manchester City were one of the direct causes for the recent Carlos Tevez spat. His agent, Kia Joorabchian, was once one of the most powerful individuals at City, through his recommendations and contacts, and it is no secret that he despises not being a shoulder for the club to cry on anymore.
City also has an abundance of strikers at the club at the moment in Tevez, Balotelli, Jo, Santa Cruz and Adebayor. Obviously, the latter trio are not rated by Mancini, but it seems an antagonistic approach to bring in their replacement now when the summer would make more sense.
Wolfsburg's situation must also be looked at.
Their main problem this term is scoring goals and selling their best player and main onion sack assassin would be nothing short of domestic suicide.
At the moment, they are nine points off the bottom of the table; on the other hand, they are only 12 points off the Champions League and if Steve McLaren can bring in one or two influential signings, there is no reason why Die Wolfe cannot climb the table.
Daniel Agger and Bayern Munich's Mark van Bommel are the latest pair to be linked with the club.
There is little doubt that Edin Dzeko will move on from Wolfsburg one day. Moving in the summer looks a far better bet than January though and Manchester City will not be the only team bidding for his undoubted talents.