The 53-year-old recently left Sheffield United with the Blades deep in relegation trouble, sitting bottom of the Premier League.
Wilder is currently favourite to become the next permanent Celtic boss with the bookies.
He guided Sheffield United, his boyhood club, from League One to the Premier League across nearly six seasons and more than 220 games in charge.
Former England goalkeeper Paul Robinson reckons the Parkhead club would be smart to choose Wilder as Neil Lennon’s replacement.
Despite some misses this season, he is seen as a shrewd operator in the transfer market with Celtic requiring somewhat of an overhaul, especially if key players depart in the summer.
“Wilder is someone who can be clever in the market,” Robinson told Football Insider.
“Yes, he did not have a great window in the summer with Rhian Brewster and others and perhaps that was his downfall. I think he would be the perfect choice for Celtic though.
“I suspect Wilder has a very good relationship with a lot of the players at Sheffield United. If he did go to Celtic and he wanted to sign some of his former players, I am sure he could.
“They are a massive club and there is always a draw. I would have loved to have done it in my career. Celtic are one of the biggest clubs in European football.”
Meanwhile, the odds on Manchester City Under-23 boss Enzo Maresca becoming the next Celtic manager have shortened and is just behind Wilder, John Kennedy and Roy Keane in the bookies’ shortlist.