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However, there has been little headway regarding any potential move since Newcastle initially stated that its star forward was off the market, with Eddie Howe insisting there has been no change to the situation on Friday.
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Newcastle, on the other hand, has yet to sign a forward to fill Isak's boots.
The Magpies are eyeing Yoane Wissa, who is currently not training with Brentford, but this seems to be a separate target from Isak's situation
Newcastle saw Callum Wilson leave at the end of his contract earlier in the summer.
The north east-based side are left with limited favourable options to resolve the dispute with Isak
The striker, who boasts 62 goals in 109 appearances for Newcastle, still has three years left on his contract.
Allardyce believes it would require fortitude from the club's board to resist selling their valuable asset.
"Sell him
Sam Allardyce reckons Newcastle have two options
Allardyce went on: "Unless the board are strong enough to say 'let him rot, Sam, we'll go and buy you another centre-forward', which is the best way to deal with it in my opinion.
"Somebody has to stand up to a player, or players, that are gonna start doing this on a regular basis, where they've got contracts - in Isak's case a particularly long contract of three years - then the owners are obviously looking not to devalue him.
"But at the end of the day if you want to stand up and be counted, put a shock across the players across the Premier League saying 'you can't treat your clubs like this after you've dedicated yourself to a contract'."
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