The former Hoops hitman, speaking exclusively to Football Insider, wants to see the attacker thrive at another club.
Johnston, 22, has only accumulated 30 minutes of action across three games this season.
Last season, he only made 10 appearances in all competitions as he suffered with a ligament injury.
McAvennie claims there is no place for Johnston at Celtic with plenty of players ahead of him in the pecking order.
“I think he’s been here too long,” McAvennie told Football Insider correspondent Ben Wild.
“He’s got to go. He’s not the kind of player Celtic want or need at the moment. Basically, he’s a part-timer.
“He doesn’t suit the style. Johnston has fallen even further down the pecking order now.
“That means he probably won’t get to play where he wants to play, which means he won’t perform as well.
“It’s bad now but Forrest is injury. When he comes back Johnston has absolutely no chance.
“There are a lot of games and maybe he can be useful from the bench. I just see the new players coming in this January and I don’t see a place for him.
“I want him to go and find somewhere he can play week in week out. He deserves that.”
The winger has made 62 appearances for Celtic in total.
He has scored 11 goals and chipped in with nine assists.