The Swede is a target for Liverpool, while he is also subject of intense interest from Saudi Pro League giants Al-Hilal.
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Isak has missed Newcastle's Asian preseason tour after making a transfer request last Thursday. However, he currently isn't at home on Tyneside.
Instead, El Diario Vasco says Isak is working regularly at Real Sociedad's facilities in Zubieta, accompanied by a personal fitness trainer.
Medical tests he underwent have revealed no injuries, fueling suspicions of a "strategic injury" to avoid public exposure before the transfer.
Newcastle initially stated Isak would miss their tour with a "minor" thigh injury before it broke that he had made a transfer request.