According to the Daily Mail, the 32-year-old was recently told to train with United's U-21s by Mourinho, who had earlier informed him he was not a part of his plans for 2016/17.
Schweinsteiger, who recently retired from international football following some below-par performances for Germany at Euro 2016, endured a difficult first season at United after a string of injuries hampered his progress.
United are currently well-stocked with central midfielders and the imminent arrival of Paul Pogba at Old Trafford has seemingly put an end to his Red Devils career.
Schweinsteiger's fall from grace at United has been further compounded after it was confirmed he had been told to turn out for the reserve team by Mourinho.
The 120-cap former Germany international has since been the subject of much transfer speculation, with the likes of AC Milan and Inter said to be interested in securing his signature.
Schweinsteiger has two years left on his United deal and could face the prospect of no competitve action if a deal is not concluded.