Hooper's form has raised a few eyebrows this season, with his performance in Moscow earlier this month even prompting England veteran Gary Lineker to take to Twitter, urging Roy Hodgson to take a look at the Parkhead forward.
Liverpool have been tentatively linked with the player, as have Fulham, Southampton and Newcastle. It is somewhat inevitable that he will eventually want to head south and test himself in the Premier League, but with Champions League football to occupy him, there is little rush.
McAvennie, who starred for St Mirren, West Ham and Celtic, has seen improvements in Hooper's game this season and has urged him to stay at Parkhead for the time being.
Peter Lawwell has been in negotiations with the striker's representatives about extending his current deal as other clubs keep tabs on his exploits, but Macca does not envisage the player being in a hurry to leave just yet.
"I have watched a fair bit of Gary and I think he looks like a player who is happy with his football this season," he said.
"He is one of the guys that Neil wants to get tied down on a long-term deal and you can see why.
"I thought his performance against Spartak Moscow was excellent, it was the perfect centre-forward's display in a game like that, and I think that he has kicked on an awful lot since he first joined the club.
"He holds the ball up better, he puts in an all-round shift and his finishing is good. Neil couldn't have bought a goal when he was playing, but he certainly knows a player when he sees one.
"During his career he played with the best of them and his management and coaching, I think, are making Gary a much better player than the one he signed.
"These are the years where he can really learn his trade and right now I think Celtic is a great club to be doing that at. It is a mutual thing – both are benefiting hugely from the other. He has got the skills required to make it at the very top, but he has plenty of time before he'll need to be thinking of making the next step."
Celtic are in the enviable position at the minute where there is no need for them to cash in on a player simply to balance books.
The sale of Ki Sung-Yueng this summer and the revenue that the Champions League will bring has offset the loss of earnings that comes with Rangers not being in the top flight.
It means then that they can pick and choose the offers they turn an ear to and puts them in a commanding position should someone come calling.
"I do know that it would cost a whopping amount of money to replace Hooper if he left," said McAvennie. "Goalscorers are what everyone will always be willing to pay for.
"Like most players, I am sure he would love to test himself in the Premier League because it is a fantastic league, but it would be silly to go somewhere that he was not guaranteed a start or somewhere where there is not a great deal of pressure on him every week to be winning.
"It is that kind of pressure that I think strikers relish. He has the Champions League just now and that is the biggest stage you can perform on in the current game.
"Everyone wants the chance to play in it and Celtic have shown this season that they are capable of mixing it.
"They are looking at a double header against Barcelona and as a player that is what you want. They don't come much better than Barca."
While Lennon has championed the striker for a call-up, McAvennie believes Hooper is still a little bit away from that level.
However, he has reiterated that if the player continues to do his talking on the park then he will make it difficult for Hodgson to overlook him.
"You look at the likes of Jermain Defoe who can't get in and you can see that Hooper might have a bit to go," said the 52-year-old.
"But if he can maintain the level he played at in the Champions League then he will make people consider him – as that is a level that is as good as international football.
"He is young, he has time on his side and he is improving all the time. What he has to strive for is a level of consistency that would mean he is playing the way he played in Moscow regularly.
"If you can do that, it starts to become second nature to you and you keep producing the goods. The boy has it in him to go far, but his best move at the minute is to continue his education at Celtic Park."