Liverpool had an offer of £110m for the Sweden striker rejected by Newcastle this week. The Toon are understood to rate Isak in the £150m class.
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BBC Sport says Liverpool regard Newcastle's assessment as unrealistic are prepared to end talks for the centre-forward.
Indeed, Liverpool insiders concede a deal for Isak this summer is now unrealistic.
For now, Isak is training away from the club after making a transfer request almost 10 days ago. The striker has been in San Sebastian, Spain, where he has been using the training facilities of former club Real Sociedad.