The 27-year-old keeper, previously linked with Manchester United, is now reportedly a target for City boss Manuel Pellegrini.
The Chilean dropped Joe Hart for the 7-0 victory over Norwich City at the weekend after a series of high profile errors. Costel Pantilimon stepped in and kept a clean sheet, but recent reports claim former-City boss Roberto Mancini - now managing Galatasaray - is keen to sign Pantilimon.
That opens the door to a possible keeper swap - although the Turkish giants expect a "substantial" cash offer for Muslera.
"I hope Muslera will stay with us for a long time to come, but if a very substantial offer comes, we will consider it," said Aysal as reported by Sky Sports.
The Uruguayan international joined Galatasaray from Lazio in 2011, and he's established himself as the undisputed number one in Istanbul.
That's more than can be said for Hart, who lost his place to Pantilimon at the weekend following his most recent clanger against Chelsea.
Mancini signed Pantilimon from Politehnica Timisoara in 2011, and although he has spent the vast majority of his City career as the back-up to Hart, he's now expected to keep his place for the Champions League match against CSKA Moscow.
The Old Trafford stopper was linked with Barcelona, but he's firmly established as the first-choice keeper at United.