Bolton appeared to be in pole position to sign the 32-year-old former German international but the Blues have nipped in and Hamann is believed to be keen to talk to City over a 2-year deal.
Should the signing go through then it would almost certainly put an end to the Blues' interest in former United midfielder Quinton Fortune, who ironically could join Bolton, and could pave the way for contract rebel Joey Barton to leave.
New Middlesbrough boss Gareth Southgate is expected to make a £3m bid for Barton, who is in the final year of his contract.
City boss Stuart Pearce would have liked the 23-year-old midfielder to stay and sign an improved 4-year deal that would have earned him up to £29k-per-week, but there have been no indications of that happening so far this summer.
Pearce, meanwhile, has not stopped his search for fresh faces and is still holding an interest in Argentina-based Peruvian Juan Vargas and Marseille teenager Samir Nasri.