The Telegraph's Richard Amofa cited "reports in Turkey" linking the Germany international with a move to Besiktas after indications that Schweinsteiger may be part of a "mass clear-out" at Old Trafford by new manager Jose Mourinho.
The Daily Record's Duncan Castles said the former Chelsea boss deems Schweinsteiger "surplus to requirements," along with Juan Mata, Marcos Rojo and Daley Blind, and he is looking to move them on to make way for "fundamental" and "supplementary" recruits.
Schweinsteiger, 31, only moved to United from Bayern Munich last summer but endured a frustrating debut season in Manchester under manager Louis van Gaal, with injury ruling him out of action from late March to the end of the campaign.