Newcastle would need to make an "extraordinary" offer to persuade Erik ten Hag to take charge at St James' Park.
The club's new owners, led by Saudi Arabia's Public Investment Fund, are on the lookout for a new head coach.
Steve Bruce departed his boyhood club by mutual consent last week, with his erstwhile assistant Graeme Jones handed the reins on an interim basis.
Jones oversaw a 1-1 draw with Crystal Palace on Saturday, but Newcastle remain without a Premier League win after nine games.
The former Luton boss is not thought to be a contender for the permanent role.
Ex-England internationals Steven Gerrard, Wayne Rooney and Frank Lampard have all been linked with the vacancy.
Paulo Fonseca is thought to be in pole position to succeed Bruce, but Eddie Howe and Lucien Favre may still be in contention.
Ten Hag emerged as a potentially candidate over the weekend, with Ajax director of football Marc Overmars linked with a similar role at St James' Park.
However, the Chronicle writes that Ten Hag is unlikely to leave the Johan Cruyff Arena for Newcastle.
The report quotes the Dutchman's own words from last week when he was asked about the possibility of Overmars moving to the northeast of England.
"Marc hasn’t informed me," he said. "I don’t think he’s withholding anything from me either. I’m not working on and now is definitely not the time."
And when the prospect of leaving his current job was put to Ten Hag on a previous occasion, he said: "There’s no reason for me to think about that now. I am very happy at Ajax and I give everything for the club, every day.
"I know you can’t plan anything in football, but you have to make an exceptional and extraordinary offer if I want to change my plans."
Newcastle would no doubt be able to offer Ten Hag a lucrative contract, but the Ajax boss is unlikely to be their next manager.
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