Per the source, Schweinsteiger will be allowed to leave and Besiktas have made a loan offer for the Germany international.
The Black Eagles are reported to have made an enquiry to the agent of the player regarding whether he is open to joining over the summer.
Besiktas would be able to offer the 31-year-old first team and Champions League football next season. The Istanbul giants are in pursuit of an experienced midfielder and currently lack depth in the position he would be deployed in should the transfer go ahead.
The Manchester Evening News also report that his days at Old Trafford could be numbered and he has not been included in the squad that travelled to China – although the reason for that is more likely that he is on honeymoon after recently marrying tennis star Ana Ivanovic.
French giants PSG are also reported to be interested in the midfielder according to the Sun.
The 31-year-old has won eight Bundesliga titles and the Champions League over an illustrious career.