The report states that the Red Devil’s will table a bid for the Uruguayan international if David de Gea agrees a move to Real Madrid in January.
Galatasaray want at least £25 million for the Uruguayan international goalkeeper.
Muslera played a key role in Galatasaray 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 29-year-old played a key role in Galatasaray’s Turkish Super Cup win over Bursaspor. Muslera has won three league titles at the Lions and also the Copa America with Uruguay.
The Uruguay international has conceded five goals in four games this season for Galatasaray.