Isak made a transfer request last week and is currently in San Sebastian, Spain, training at Real Sociedad's HQ as he waits for Newcastle and Liverpool to find terms over a fee for him.
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United, reports Sky Deutschland's Florian Plettenberg, made an enquiry this week - and received an instant negative response from Isak's camp.
Liverpool have had a £110m offer for Isak rejected by Newcastle in recent days, with the Toon insisting he won't leave for less than £150m.
Plettenberg also states Isak and Liverpool have agreed personal terms over a contract to 2031.