Fanatik says the two clubs are said to have agreed over the basis of a transfer fee of €5m, with the move to take place immediately upon the summer transfer window opening.
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Bayindir has been with United since January 2023 and has made six Premier League appearances this season.
United signed the 27-year-old for a fee of €5m from Besiktas rivals Fenerbahce.
With Besiktas, Bayindir is expected to receive a salary of €2m.