Forster, who has one England cap, is 31 minutes away from breaking the Scottish top-flight record for clean sheets, and Ambrose feels the 25-year-old is improving all the time.
The Nigeria centre-back said: "He is young and hungry for success. He is doing better than last year and he is improving every game he plays.
"I believe in a couple of years he will be the best in England. He can be the best in the world and right now he is one of the best."
Forster has kept 12 consecutive SPFL Premiership clean sheets and can break former Aberdeen goalkeeper Bobby Clark's record during Saturday's game against Hearts at Tynecastle.
But, despite his praise for Forster, Ambrose believes all of Neil Lennon's team deserve credit for the feat.
"It's fantastic," Ambrose said. "It just shows how dedicated we are in the team and how the hard work pays off on the pitch.
"Credit goes to the team and everybody that made it possible. It's a team game. We have to do it from the strikers, midfielders, defenders and goalkeeper. Everybody is doing their bit."
Ambrose was speaking as Celtic stars who hope to be heading to this summer's World Cup in Brazil backed the Project Fair Play initiative which will see thousands of football shirts being sent to disadvantaged kids in the South American country.
Ambrose said: "Project Fair Play is a great idea to send unwanted kit to people in Brazil who may never get the chance to buy their own.
"The project aims to bring football to children in as many areas of Brazil to make sure they don't miss out.
"Project Fair Play will make this year's World Cup even more special as we enjoy the excitement of games, knowing that it is helping to make football a fantastic experience for disabled youngsters in the UK as well as those living in Rio.
"Celtic and our players are delighted to be supporting this initiative."
Stay in touch with all the latest developments on Facebook or follow the campaign on Twitter @projectfairplay