The BBC reported that the Spanish international “is expected to stay at Old Trafford beyond the end of the transfer window.”
The Red Devil’s are understood to be preparing a £24.5 million bid for Muslera if De Gea departs United in favour of Real Madrid according to the Metro.
Muslera joined Galatasaray back in 2012 in a part-exchange deal from Lazio.
The 29-year-old a key role in the Lions winning the league for a record 20th time last season and earning the right to wear a fourth star – Galatasaray also won the double for a record sixth time.
The experienced goalkeeper was voted as player of the season by the Turkish footballers union on Monday. Muslera has won three league titles at the Lions and also the Copa America with Uruguay.