Forster has been a key performer for the Hoops this season and has been particularly impressive on the European stage, as Neil Lennon's men aim to secure their progression to the last 16 of the Champions League.
Former No 1 Bonner had doubts over the Englishman initially, but now sees potential in the 24-year-old to become a Celtic great in his own right.
"I've been very impressed by him – no question," said Bonner.
"I've actually been surprised by how well he's done, considering there were a few doubts when he came in at first. It's all down to him, it comes from the person himself.
"He's had the intelligence to take in the information from his coaches, he's worked hard at his game and the results are there for everybody to see.
"Great credit must go to him for how he has responded and matured and put himself into a situation where he'll be regarded as a great Celtic goalkeeper in years to come if he keeps producing what he's producing now."
Forster signed a permanent deal in the summer after a loan spell in the east end of Glasgow while at Newcastle. And Bonner – who made over 640 appearances for Celtic – has been impressed by how well he has adapted to life at Parkhead.
"He is a top-class goalkeeper but when you play with Celtic, or any of the big clubs who dominate games, it's a different type of game than playing in a game where you get 10 shots, make six great saves and walk away from the game getting beat but having played well," he said.
"At Celtic, you can't afford to make mistakes, you need to keep the concentration levels. You might have one or two saves to make in a game and you have to do it 100pc.
"That's what you learn and he has learned how to play in a Celtic team. But he has also shown when he's under pressure and having to make the saves, that he can do that.
"He is a top-class goalkeeper. Whether he becomes a legend, that comes with time and experience and playing 400 or 500 games and winning championships and being the main guy in that team and having people talking about him for years to come.
And former Republic of Ireland goalkeeper Bonner urged him to be ready when the chance comes for his first cap.
"He's got competition with Joe Hart, who's a young goalkeeper too and he's playing with Manchester City. But he has to be ready for the moment when it comes. When he does go in, he has to perform," said Bonner.
"For him, it's fantastic for the confidence to be in the England squad and at that level."