The Daily Mail says Dzeko actually wrote to City in the summer admitting he wanted a move to Eastlands.
In public Dzeko has been coy about his future while Italian clubs such as City's Europa League rivals Juventus have briefed Italian journalists that he wants to move to Serie A.
However, one of his representatives was a guest of City at last month's Manchester derby which, allied with this latest development, suggests City are in pole position.
One thing that will certainly influence Dzeko's thinking is the fact that Wolfsburg are currently having a difficult season and are fifth from bottom of the Bundesliga.
Dzeko has scored eight league goals in 16 games but recently had a public spat with McClaren, ignoring his manager's outstretched hand after being substituted against Werder Bremen earlier this month.