The 55-year-old spent three years at the start of his playing career at Celtic Park during the 1980’s.
Moyes has been out of work since last May, when he parted ways with West Ham United.
But now the former Manchester United boss is seeking a return to management in the summer.
Having been linked with the Scotland job after their shock 3-0 defeat to Kazakhstan, Moyes confirmed he is more interested in club football for his next project.
“Club football would be my choice, but Scotland’s my country and I’m really passionate,” Moyes told the BBC.
“I’ve followed Scotland to all the tournaments when I was a young man, I used to go to Wembley regularly with my dad, so I’ve got some great memories of being a Scotland supporter.”
Celtic will be looking for a new permanent manager this summer if Neil Lennon is not offered a contract to replace Brendan Rodgers, who left for Leicester.
And Moyes confirmed he’d be interested in taking over the reigns in Glasgow.
“I would always be interested, but Lenny’s done a brilliant job. He’s been there before and the job he’s doing at the moment would warrant being the Celtic manager. He’s doing a good job,” Moyes said.
Celtic fans did not seem to welcome the idea on Twitter, in the wake of his comments.
One fan tweeted: “Don’t want Moyes near Celtic, he has been found wanting at bigger teams and tactically inept when asked to attack, very defensive minded coach, times have moved on!”
Another put it plainly: “I DO NOT WANT DAVID MOYES AS CELTIC MANAGER.”
A third claimed: “David Moyes wants the Celtic gig. And I wouldn’t mind dating Sophie Turner. Let’s see who gets lucky first.”
Moyes is looking to rebuild his reputation as a coach, after disappointing stint at United, Real Sociedad, Sunderland and West Ham.
“If they appointed Moyes Celtic Park would be half empty,” another tweeted.
One fan lives in hope that they may get Rafael Benitez upon the expiry of his Newcastle contract.
They said: “Moyes can also stay away from the Celtic job. Would rather Rafa.”
