The Magpies are still searching for their replacement for Steve Bruce following his sacking.
A £305million takeover was completed last month by the Saudi Public Investment Fund, with the club now boasting the richest owners in world football.
A number of names have already been linked to the job with Unai Emery emerging as the frontrunner, before he decided to rebuff Newcastle and stay at Villarreal.
It has been reported that a sack clause in any potential contract put the Spaniard off.
Newcastle are precariously placed in 19th place after 10 games and whoever gets the job will have a tough task on their hands.
Eddie Howe is now considered the favourite, with reports that talks have begun with the former Bournemouth manager, while Frank Lampard and Steven Gerrard have both been mooted.
Former Newcastle manager Allardyce joined talkSPORT on Thursday morning to give his verdict on the current situation at his old club.
He told the talkSPORT Breakfast: "I don't think Steven [Gerrard], at this stage, will leave Rangers where they are, top of the league and winning every week, to fight at the bottom of the Premier League.
"The Premier League is a massive and exciting league that everybody wants to manage in across the world, I would presume he would want to get here someday.
"At the moment, the Newcastle job is a massive one, but why leave Rangers who are winning every week to challenge yourself with the trials and tribulations of Newcastle?
"Even though they have got plenty of money to spend, they can't spend it that quick because of Financial Fair Play.
"Whereas Frank [Lampard], if I were him I'd jump at the chance.
"He's rested, gained the experience from Derby for Newcastle, his first season at Chelsea, with very tight restrictions, got them to the Champions League.
"Then when they spent the money and they didn't gel, he was gone.
"If the club has got money, there's not a better place for Frank than to take Newcastle on.
"Maybe that might be the owners' view and it would be nice to see a British manager taking over any Premier League club."