The daily sports paper states that the Istanbul Giants are looking to sell their star assents to ease the financial situation at the club.
Galatasaray have been banned from European competition next season due to failing to meet Financial Fair Play regulations.
Muslera was also linked with a move to Manchester Untied over the summer before David de Gea signed a contract extension.
Muslera recently recieved a bid from the Argentinain side River Plate. However, the Uruguayan international revealed that he turned down the offer.
Muslera told Fanatik: “It is an honour to get an offer from River they spoke with my agent but I have a contract with Galatasaray until 2018.”
The Uruguay international a key role in Galatasaray winning the league for a record 20th time last season and earning the right to wear a fourth star – the Lions also won the double for a record sixth time.