On Friday, United boss Jose Mourinho revealed that Ibrahimovic would remain on the sidelines through injury until the end of January, but it appears that there are no guarantees of the Swede still being at Old Trafford.
According to Fotomac, both Besiktas and Galatasaray intend to offer the 36-year-old regular action in Turkey during the second half of the campaign.
Despite returning from a serious knee injury during the middle of November, Ibrahimovic has made just two starts and five substitute outings in all competitions and is now unlikely to be regarded as first-choice striker by Mourinho.
Besiktas have space and funds available for a frontman with Everton having signed Cenk Tosun earlier this month, while Galatasaray have shown in the past that they like to attract big names to the club, regardless of the stage of their career.
Ibrahimovic's contract at United expires in the summer.