The 21-year-old has been on City's radar for some time and they are thought to be nearing an £11million swoop for the versatile defender.
Blues boss Roberto Mancini confirmed City's interest last week and it is understood the ambitious Premier League outfit are now deep in negotiations with Hamburg.
Boateng started out at Hertha Berlin and moved to Hamburg in 2007, becoming a regular both in domestic and European football. He has since been rewarded with three appearances for Germany and has been named in their provisional World Cup squad.
Boateng would be the third Hamburg player City have signed in recent years having bought Vincent Kompany in August 2008 and Nigel de Jong in January 2009.
He is also the younger brother of Portsmouth's Kevin-Prince Boateng, who has become a hate figure back home after his challenge on Chelsea's Michael Ballack ruled the Germany captain out of the World Cup with an ankle injury.
The Boateng brothers have a German mother and a Ghanaian father, and Kevin-Prince has pledged his allegiance to Ghana after representing Germany's Under-21s.
And the Berlin-born pair could come face-to-face at this summer's World Cup as Kevin-Prince has been named in Ghana's provisional squad and Ghana and Germany will face each other in their final group game on June 23.