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The former Scotland winger admits alarm bells are ringing around Parkhead, with supporter frustration boiling over amid a poor run of form.
Recent protests against the club hierarchy have underlined the anger among sections of the support, and Nevin believes the mood around Celtic has become a major concern.
Speaking to CasinoHawks, he said: "Everyone's questioning it. There's turmoil in the fanbase, absolute turmoil.
"They've turned on the club. A group of Celtic fans turning up and throwing tennis balls onto the golf course when the owner was playing in a big tournament.
"I know it doesn't sound that extreme, but if you start chasing people outwith the game, I don't think Celtic fans know how serious that is. That's extraordinary."
Supporters have demanded change from major shareholder Dermot Desmond and the club's leadership, with Nevin warning the protests appear to have moved beyond football matters.
He added: "They want change from Dermot Desmond, they want change from there, but going into personal life, that's a jump, that's a step change."
The backdrop to that discontent is a miserable spell on the pitch, with Celtic struggling for results and confidence.
Nevin believes the coming weeks could make or break the Hoops' season.
He said: "It really is going to be some month because Celtic are on a terrible run at the moment.
"They've just played Benfica, then it's Hearts at home, which is never going to be easy. They've got Celta Vigo coming and then Hibs away.
"Hibs are not in a great time, but they're always a tough team to play at Easter Road."
The pundit feels manager Martin O'Neill now faces the difficult task of steadying the club both on and off the park as noise continues to grow around the champions.
He said: "Martin has to bring all of that together. To be honest, is anyone better at doing it than Martin? Probably not. But it's still a big job."
Despite the current gloom, Nevin urged supporters not to lose sight of Celtic's recent dominance.
He added: "This is the club that's won 14 of the last 15 championships. It's concerning, but let's keep it in perspective. I think other clubs have got bigger problems."