The 34-year-old's future was brought into focus after he revealed that he has yet to be offered a contract extension by the Reds, with his current deal due to expire next summer.
The European Cup-winning skipper insisted that he would not be retiring, though and also indicated that he would consider a move away from Merseyside in order to prolong his playing career.
The Daily Mail claims that the Premier League champions are interested in signing the ex-England international captain as Manuel Pellegrini looks to increase the number of homegrown players in his squad.
It is also thought that recruiting Gerrard would be a boost to City, who are hamstrung by Financial Fair Play rules and are believed to be on the hunt for transfer bargains, such as the loan move which brought veteran midfielder Frank Lampard to the Etihad Stadium on loan.
Gerrard was part of the Liverpool team which lost 1-0 away to Newcastle United on Saturday.