The 25-year-old goalkeeper joined Celtic on a permanent deal after spending the previous two years on loan at Parkhead.
But he admits he has not given up on his dream of playing for the Magpies, and said: "I'd like to go back to Newcastle at some point, if the opportunity arises.
"I'm a Newcastle fan and I've got unfinished business there. It was a wrench to leave, it's my hometown club. But it wasn't meant to be.
"I enjoyed my time out on loan and after enjoying playing week in week out it was important I carried on playing. I wanted to be number one and it was clear that wasn't going to happen at Newcastle."
He also admits that, despite loving his life in Glasgow with the Scottish champions, he would like to play in the Premier League.
"Everyone wants to be playing in the Premier League. It's the place to be," he said.
"At the minute I'm very happy at Celtic and playing Champions League football, but long-term it would be nice to play in the Premier League."
Forster has won international recognition this season after being called up to the England squad by Roy Hodgson and he firmly believes he can push for a place at next year's World Cup should the Three Lions book their place in Brazil.
"It's the World Cup next year and I'll be giving it my all to try to get in the squad,' Forster told Late Kick Off.
"It's important to be playing at the highest level I can. Celtic is a fantastic club and European football is the pinnacle. Now it's all about getting as much experience as possible and getting in the England squad."