The Turkish champions offered the 31-year-old around £18.3 million a year tax-free, but Fernandes has made clear he wishes to remain with United despite the chance to significantly increase his earnings.
Manchester United have entered preliminary talks with the Portugal international, who has entered the final year of his current contract, which includes the option of a further 12-month extension. Well-placed sources say there is no rush to get a new deal over the line, though discussions have begun.
Fernandes signed his current contract in 2024, and his £57 million release clause for overseas clubs expired last month. United plan to reject any offer for their captain and have not received any concrete contact over the reigning Premier League Player of the Season.
Galatasaray had been intending to table an offer worth around £42.8 million for Fernandes, who turns 32 next month. Club president Dursun Özbek has been overseeing the audacious push and is understood to be determined to sign the midfielder, with Galatasaray reportedly willing to offer a four-year contract worth £18.3 million annually, plus a further £3 million up-front signing-on bonus.
Turkey's favourable tax system means Fernandes could double his current take-home pay were he to make the move.
Fernandes joined United from Sporting CP in January 2020 and has gone on to become one of the club's most influential performers, taking over the captaincy and being named the division's standout player last season. His preference to stay, allied to United's refusal to entertain offers, leaves Galatasaray facing an uphill task to turn interest into an actual transfer before the market closes.
Fernandes previously turned down the chance to move to Saudi Arabia twelve months ago, rejecting interest from Al-Hilal in favour of staying at Old Trafford, and has consistently spoken of his desire to help restore the club to the level its history demands.
Turkish interest in Premier League stars has grown increasingly aggressive this summer, with several English clubs having fielded approaches for key players as Süper Lig sides look to leverage favourable tax rates to lure established talent away from England. United's stance, though, remains unambiguous: whatever Galatasaray table, their captain is not for sale.