After having a club record bid of £110m rejected by Newcastle over a fortnight ago, The Telegraph says the Reds intend to go higher before Monday's transfer deadline.
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Discussions over the potential sale of Isak have progressed in the last 24 hours betwee the two clubs.
Liverpool's board have now agreed to make a massive £130m proposal to Newcastle for the wantaway Swede.
It still falls short of Newcastle's £150m valuation, but there is hope they will soften their stand with a deal for Isak's replacement now close.
Newcastle and VfB Stuttgart have agreed terms over Nick Woltemade, who could be on Tyneside today to complete the move.