However, Newton feels another ex-Chelsea man may be more suited to the job.
"He has done extremely well with Scotland and extremely well in the Premier League, he has been a Championship manager and now he's a national team manager so he has the pedigree to go into Celtic," Newton told Sky Sports about Clarke.
"I know him personally. He is a fantastic character who doesn't mince his words. A typical Scottish guy who doesn't mince about with his words.
"But he is a good guy and right at this present moment he would be a very good candidate for Celtic."