The Parkhead icon, speaking exclusively to Football Insider, claims “the money is there” to sign a “top-quality” defender.
Celtic have been rotating Greg Taylor, Josip Juranovic and Boli Bolingoli in the left-back position this season.
McAvennie insists Celtic will fix this “problem position” in January.
“Left-back is the problem position,” McAvennie told Football Insider correspondent Ben Wild.
“We just can’t seem to get it right. I don’t think Postecoglou is happy.
“Juranovic is a right-back but he plays left-back quite a lot of the time.
“Taylor is in and out and Bolingoli can’t get more than a couple of games even though he’s the best of the lot.
“That tells me Ange isn’t completely happy and I think a new left-back will be first through the door in January.
“I think we will spend, the money is there. The defence is definitely the problem.
“But the same centre-backs start every week and it’s usually Ralston at right-back.
“A top-quality left-back would improve us to no end.”
They are next in action against Ferencvaros in the Europa League on Thursday.