According to transfer expert Ben Jacobs, Newcastle chiefs feel Isak will either leave the club this summer or sign a new contract as they view it as untenable that he will stay on his current terms.
Newcastle have already tried to convince Isak to sign a new contract and have promised him he can leave next summer.
Meanwhile, Liverpool do not plan to submit a second bid for Isak at present unless Newcastle offer encouragement. But if the Magpies open the door for a deal to take place, the Reds will be there to pounce.
Isak’s future is said to hinge on whether Newcastle can find a replacement for the blockbuster star and how hard he pushes for a move away from the north east.
Newcastle are currently pursuing the signature of RB Leipzig striker Benjamin Sesko, who has bagged 27 Bundesliga goals during two seasons in Germany.
But Eddie Howe’s side reportedly saw an offer of £65.5m plus £4m in add-ons turned down on Saturday as Leipzig were unhappy with the overall package.
And Newcastle also face competition from Manchester United for Sesko’s signature, with the Slovenia international said to be impressed by the Red Devils after being made aware of Ruben Amorim’s long-term plans.
Isak has landed back in England after training on his own at the headquarters of his former club Real Sociedad.
According to Sky Sports, the player himself refused to join the Newcastle squad on tour in the Far East and opted to head to Spain to train with his own staff instead.
The Magpies are said to value Isak at £150m but don’t want to sell him, with the prolific goalscorer still having another three years remaining on his current contract.