Per the source, Schweinsteiger, Tyler Blackett, James Wilson, Will Keane, Paddy McNair, Cameron Borthwick-Jackson and Adnan Januzaj face the axe while Andreas Pereira and Guillermo Varela are likely to return to the club after their loan deal.
Mourinho wants to trim down his squad to 22 players and wants to make way for the arrival of Paul Pogba who is set for a world record £112 million transfer to Old Trafford.
Schweinsteiger is being targeted by Turkish champions Besiktas who have been tying to loan the 31-year-old midfielder.
The Milliyet newspaper report that the Istanbul giants have been preparing a move for the World Cup winner in an attempt to bolster their midfielder ahead of the Champions League.
Besiktas could be prepared to sign Schweinsteiger on a free transfer or for a reduced fee if United were to agree.
The Eagles won the league title last season and will compete in the Champions League group stages.