The Premier League side are still looking for a replacement for Steve Bruce after he was axed last month.
Newcastle's new owners have been weighing up their options, knowing who they hire is the biggest decision they will have to make of their short regime so far.
The Magpies currently sit second from bottom and will need someone to steer them away from that fight.
Emery and Eddie Howe were said to be the frontrunners for the job, but the former Arsenal boss is firmly out of the race.
The Mirror report the clause Newcastle wanted in the contract led to him rejecting the role.
The news the Spaniard is out of the race will be a blow to the new owners with Eddie Howe now in the frame.
Former Newcastle manager Sam Allardyce joined talkSPORT Breakfast on Thursday to give his verdict on the situation.
He believes the new regime may have a tough time appointing the calibre of candidate they want to due to their current league position.
Allardyce told talkSPORT: "For Newcastle, the choice of manager is critical. What do they want at this moment in time and how do they get him?
"A top manager like Emery looks at Newcastle near the bottom of the Premier League and thinks 'do I really want that challenge?'
"That's the problem they have. They might well have the money now or better money to spend, but a manager of his quality does he look and think and say yes they've got plenty of money but look at the project and the rebuild that Newcastle need to be a great side challenging at the top of the Premier League.
"I think it is the time that takes and the money that takes where the problem is going to lie.
"The new owners will have a problem finding the right man to take them forward, it's very, very difficult indeed I would say."