The Liverpool skipper has recently spoken to the press about the possibility of playing his football away from Anfield should the Reds not offer him a new contract.
Reports do suggest, however, that Liverpool will offer Gerrard a new deal if he is willing to accept less playing time on Merseyside.
But City boss Manuel Pellegrini has spoken highly of the the 34-year-old and the Mail claim that the Manchester club hold an interest in bringing the veteran to the Etihad Stadium, just as they have done with Chelsea legend Frank Lampard this season.
Meanwhile, the same paper also claim Gerrard is a target for an MLS side.
Needless to say, the ongoing speculation has prompted quite a response from Liverpool fans. And it is a mixed response, it has to be said.
A definite majority of Reds fans would be sad to see their captain leave for a Premier League rival, while many believe it simply won't happen.
Others, however, feel Gerrard deserves a league title - and has no chance of getting one at Anfield. At the same time, some Liverpool fans also feel the 34-year-old is past his best and would encourage him to leave Merseyside.
Here are the best supporter reactions to the reports on Twitter. What a shock move it would be...
Favourite this now. If Gerrard, EVER plays for Man City, I'll run through town with nothing but a Kolo Toure mask on.— Becci (@BecciBoopLFC) November 1, 2014
If we somehow manage to lose Steven Gerrard to City I am pretty sure the entire fan base will have a riot #LFC— John Lombard (@JLombard207) November 1, 2014
Need to sort out this Gerrard business. Rough time for lfc and everyone associated worst possible time for all of this— Matt Kane (@matt_kane8) November 1, 2014
Steven Gerrard should move to Man City next season. He deserves a Prem league medal & won't get it while at Anfield #LFC Pains me to say— Dave King (@DaveTheKing21) November 1, 2014
Gerrard to Man City? Would help us out, they could do with getting worse.— Ryan (@RyanMcTrippy) November 1, 2014
If Gerrard's decided he wants to leave, I honestly don't blame him. He's been patient long enough— #ForzaJules (@Kershaw16rob) November 1, 2014
The Gerrard talk is getting out of hand. He'll be playing for Liverpool next season. Deal with it.— Andy Young (@AYPrivateEye) November 1, 2014