Forster is in the second season of a four-year deal, but he cast doubt over his long-term future after his side ended their European adventure with a 6-1 defeat by Barcelona on Wednesday.
When asked whether he expected to still be at Celtic when their next Champions League campaign begins, Forster said: "I don't know. There's a lot of time between now and then.
"It is hard to say either way. Obviously I'm contracted to Celtic and I will be for the foreseeable future, I imagine.
"It is just important that I do the best I can do, whether it is for Celtic or whoever."
The 25-year-old made his international debut in England's friendly defeat by Chile last month and is determined to seal his place in Roy Hodgson's squad for next summer's World Cup in Brazil.
"I've just got to be positive and do everything I can between now and the end of the season to try and force my way on to the plane with the England squad," the former Newcastle player said.