The report claims that United are targeting Muslera as a potential replacement for David De Gae should he part ways with the club over the summer.
De Gea has been closely linked with a move to Real Madrid according to the Marca.
The report claims that United want €40 million for the Spanish international keeper but a deal is yet to be agreed.
Galatasaray want to keep hold of Muslera but could be forced into considering such a substantial offer.
Muslera played 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 keeper has won three league titles at the Lions and also the Copa America with Uruguay.
The Uruguayan international keeper kept five consecutive clean sheets – all of which ended in victories – at the most critical stage in the season.