The report states that the Premier League giants held talks with Galatasaray for the Uruguayan international but were turned down.
The Turkish newspaper Fanatik claim that the Istanbul giants are wary of offloading two fan favourites Felipe Melo and Muslera in one transfer window.
United are understood to be preparing a £24.5 million bid for Galatasaray goalkeeper Muslera if David de Gea departs Old Trafford in favour of Real Madrid according to the Metro.
Muslera joined Galatasaray back in 20122 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.
Muslera has won three league titles at the Lions and also the Copa America with Uruguay.