That is according to Turkish paper Millyet, who report that Aziz had emerged as a target for the Potters but ultimately decided against leaving Turkey to play in England's second tier.
They also claim that the defender's name was brought up during negotiations over Badou Ndiaye. Stoke were ready to offer the player a €2.8m contract and a four-year deal - which would have marked a huge raise in pay - however, they were turned down as Aziz opted to remain with Galatasaray.
The Super Lig side weren't willing to sell the player either, given that they need strong defenders in their side for the present campaign in which they will look to defend their league title.
Milliyet'in haberine göre Serdar Aziz, Championship ekiplerinden Stoke City’nin yıllık 2.8 milyon Euro'dan 4 senelik teklifini kabul etmedi. pic.twitter.com/RmQTwSRWeK— Galatasaray Gazetesi (@GsGazete) August 11, 2018
Millyet, though, have suggested that the club could look to sell him next summer if he gives a good account of himself in the Champions League this season.
The 27-year-old centre-back, who began his career playing for Bursaspor in 2000, moved to Galatasaray in 2016. He has won two Super Lig titles in his country, the first with Bursaspor back in the 2009/10 season and the second with Galatasaray last term.
The Turkey international made 27 appearances for the champions last season and contributed on the offensive front with one goal and one assist. He also picked up eight yellow cards.
Aziz has already started this campaign on a positive note, scoring a goal for Galatasaray in their first match of the new season on Friday and helping them to a 3-1 win over