The club’s managerial hunt could stretch into a third week after leading candidate Unai Emery opted to remain at La Liga side Villarreal.
Eddie Howe is the new frontrunner but the new owners have gone back to the drawing board, with the likes of Roberto Martinez, Paulo Fonseca and Lucien Favre also considered.
Liverpool legend Gerrard was strongly linked with the role on Tyneside during Steve Bruce’s final days at St James’s Park but Allardyce has questioned why he’d leave the Scottish Premiership champions.
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He told talkSPORT: “I don’t think Steven, at this stage, would leave Rangers where they’re top of the league and winning every week to fight at the bottom of the Premier League.
"The Premier League’s a massive exciting league that everybody wants to manage in across the world, so I’d presumed he’d want to get here someday.
"But at the moment, Newcastle, the massive job that it is because of the position they’re in… why leave Rangers where you’re winning every week to challenge yourself for the trials and tribulations of Newcastle United?
"Even though they have got plenty of money to spend, you can’t spend that quick because of Financial Fair Play I don’t think.”
Indeed, Allardyce believes Lampard should throw his name into the hat.
Lampard was sacked and replaced by Thomas Tuchel at Chelsea in January, and has been out of work since.
Allardyce added: "If I were Frank (Lampard), I’d jump at the chance. He’s rested and gained the experience from Derby and Chelsea, where his first season was brilliant under very very tight restrictions.
"Then, when they spent that bit of money, and they didn’t gel and he was gone. Of course, he needs to fight back.
"If the club’s got money, there’s not a better place for Frank to take Newcastle on. It would be nice to see a British manager take over any Premier League club for me.
Allardyce was Mike Ashley’s first manager at Newcastle before being sacked after just 24 games.