The colourful former Celtic striker believes that a decision to remove the Norwegian coach has already been made as a result of his style of play and failure to reach the Champions League group phase.
And he has cautioned Deila that if he does lose to Rangers, he should not go out in Glasgow without considerable protection.
McAvennie said: “The decision’s already been made on that, don’t you think? To me there are three people who can make the decision – Dermot Desmond, Peter Lawwell and the supporters.
“The supporters will turn out in force for this one and I just can’t comprehend Celtic getting beat, because it wouldn’t be a good city for Ronny.
“He’s got to change the way he plays. I just don’t understand this one up front in Scottish football. I can understand it in Europe but against teams in Scotland, especially at Celtic Park, play two up front and get the fans back.
“Start playing entertaining football. It’s not been very entertaining recently. The fans have stayed away because of that – no other reason.
“They’ve bought their season tickets but they’re not going to games. Ronny can stay if he wants as long as he learns from it – but he doesn’t seem to be learning from it.
“I don’t know who the second striker is – I don’t think they’ve got one. Kazim-Richards is too volatile to play in an Old Firm game. He could even beat my record of 14 minutes for getting sent off. That would be interesting, wouldn’t it?”
McAvennie feels Rangers are a lot stronger – and he welcomes their return to the Premiership – but he still believes Celtic will prevail with some comfort – although he insists it is vital that Kris Commons, pictured right, is in the starting line-up.
He said: “I don’t see them not winning. I just can’t. I’m very concerned that Rangers are improving all the time but if the real Celtic turn up and play to their capabilities they will beat Rangers. There is no two ways about that.
“If I was a Celtic striker now I would fancy my chances on Sunday.
“I like Leigh Griffiths as a striker and he’s the best they’ve got. But the biggest thing for Celtic this weekend is with a confident Griffiths up there, you’ve got to get Commons on the park. I just don’t understand – and I’ll never understand – why he’s not playing.
“In my humble opinion he’s the best player Celtic have got. He can open up defences. If Leigh gets left facing two at the back – because the Rangers full-backs bomb on – then Kris is going to find him.
“Celtic are a better team but if they turn up as lacklustre as they have been in recent times they could be in for a shock.”