The former Hoops hitman, speaking exclusively to Football Insider, wants the defender to keep his place in the side.
Bolingoli, 26, has made two appearances for Celtic this season after being sent out on loan during 2020-21.
The defender joined Istanbul Basaksehir after breaking lockdown rules and travelling abroad without telling the club at the start of last season.
He was given his first outing of the campaign during last month’s clash against Livingston and also started against Motherwell at the weekend.
McAvennie insists Bolingoli is the best left-back at the club and wants him to keep his place this weekend.
“Bolingoli is one I have been very impressed with,” McAvennie told Football Insider correspondent Ben Wild.
“He is the best left-back at the club, so why not play him? He made a mistake, we know that.
“The boy went to Spain to meet some friends and to have a party, who hasn’t made those mistakes?
“He’s miles better than Taylor in my opinion and he’s better than Juranovic when he plays left-back.
“He’s more of a defender, he doesn’t go missing like some of the other players we have.
“I hope he keeps his place.”
Celtic face St Johnstone on Saturday as they look to record a third straight win in the league.
Bolingoli should be fully fit after playing no part against Ferencvaros on Tuesday.