The tabloid newspaper states that United boss Louis van Gaal is considering leaving the Spanish international on the bench until his future is resolved.
De Gea has been closely linked with a move to Real Madrid throughout the summer transfer window and the Daily Star claim that the 24-year-old is ‘desperate’ for a move to the La Liga giants.
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.