Per the source, Schweinsteiger, Marcos Rojo and Matteo Darmian are all expected to leave.
Meanwhile Juan Mata, Memphis Depay, Adnan Januzaj and Ashley Young could be set for a summer exit.
United boss Jose Mourinho wants to trim his squad down to around 23 players and will have to sell in order to get near his target.
The report states that Turkish league champions Besiktas are in the race for the Germany international.
Besiktas are in pursuit of of a central midfielder this summer with Champions League football round the corner.
The Istanbul giants won the league title last season but lack depth in midfield and have made strengthening the position over the summer.
PSG are also in the race for the experienced Germany international according to the Sun.
The report claims thatUnited are willing to let Schweinsteiger leave but he wants all of the £14 million he is set to receive over the next two-seasons if he does part ways.