Klaassen, who arrived at the English club last summer from Ajax, has struggled this season, struggling to establish himself in the first team.
The Dutchman was brought in by compatriot Ronald Koeman for £23.6m, but he made just seven league appearances, and was offered out for a loan deal in the January transfer window.
The playmaker rejected an offer from Napoli, but 'Sky Sports' are now reporting that a loan move may be on the cards again now. According to the English outlet, Besiktas are interested in bringing Klaassen in on an initial loan deal, with a view to a permanent transfer dependent on how it goes for the midfielder in Turkey.