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 Scottish 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."