The Turkish champions have tabled a proposal worth around ten million euros for the 31-year-old Brazilian, who has spent eight trophy-laden years at the Etihad, but the Premier League giants are holding out for a higher fee to sanction his departure.
Transfer expert Fabrizio Romano revealed the development on X, stating: "Galatasaray send first official bid to Man City for Ederson. Proposal in the region of 10m Euros while City ask for higher fee."
Ederson has been linked with moves to clubs in Turkey and Saudi Arabia throughout the summer, and sources indicate he has now expressed a desire to join Galatasaray, prompting Manchester City to open talks with Donnarumma's representatives as a replacement.
Negotiations between the clubs are underway, with Ederson reportedly waiting for City to finalize a deal for the Italian before completing his own switch.
Pep Guardiola has publicly affirmed Ederson's status as his number one goalkeeper "right now" and confirmed he was "fit" ahead of their Premier League opener against Wolverhampton Wanderers.
However, the Brazilian did not travel for the match, with summer signing James Trafford set to make his debut between the posts.
Guardiola has said: "Ederson didn't come to me and say I want to leave or I have an offer. All the players are here and are our players and I work with them… What's going to happen, nobody knows!"
Sky Sports reporters have noted that Manchester City want Ederson to stay and remain their first-choice keeper, but if a suitable offer arrives before the deadline, they will consider it, provided they secure a replacement. Donnarumma, long tracked by City, tops their shortlist, though no negotiations with Paris Saint-Germain are active yet.
One source even suggested to Sky Sports News that the 26-year-old has been eyed as a potential free agent next year.
Donnarumma, meanwhile, has confirmed his impending exit from PSG in an emotional statement posted on Thursday, expressing disappointment at being sidelined. "To the special Paris fans, From the first day I arrived, I gave everything, on and off the pitch, to earn my place and defend the goal of Paris Saint-Germain," he wrote.
"Unfortunately, someone has decided that I can no longer be part of the group and contribute to the team's success. I am disappointed and disheartened."
He added hopes of a proper farewell at the Parc des Princes, thanking supporters and teammates for their backing.
Romano has added that Donnarumma "has already opened doors to City move, no issues on personal terms. If Ederson leaves, Donnarumma can join #MCFC."
With Trafford already arriving from Burnley, City appear prepared for upheaval in goal, but Ederson's potential exit would trigger this high-profile chain reaction as the transfer window edges toward its close.