The 43-year-old took the Cherries from League Two to becoming an established top-flight club in the space of five seasons before they went down after a wretched post-lockdown run.
Howe’s only other previous managerial role was a brief stint at Burnley, but reports believe that he would be interested in the vacant job in Glasgow, with Celtic still searching hard for a replacement for Neil Lennon, who was sacked last month.
And McAvennie, who spent four seasons at Celtic Park across two separate spells, described Howe as a “great coach” but admitted that his former side need a complete clear out in their backroom staff department, including current caretaker manager John Kennedy.
He told Football FanCast: “I think Eddie’s got good pedigree. He’s a young coach. Unfortunately, I think today’s game, players are too soft. They don’t take to people shouting at them, and I think that’s what happened with Lenny.
“I think Eddie Howe is a great coach, he’s done wonderful at Bournemouth, but he would have to bring his own backroom staff. Celtic need a total clearance.
“John Kennedy is up there with one of the favourites, but I don’t think the fans will want John [Kennedy] to be the manager. He’s been there for four managers, but I think it’s time John went away and got a manager’s job. Celtic is too big a club for him to cut his teeth on.”