Newcastle United cannot recall Forster, who is on loan to the Tims, until January - despite Steve Harper being ruled out for three months.
The Hexham-born keeper is on a season-long loan and while the Magpies cannot recall him at the moment, there is scope to do so in the new year.
Neil Lennon (Celtic boss): “I’m very happy with the three goalkeepers we have (Lukasz Zaluska and Dominic Cervi are the others).
“They’re pushing each other for a first-team place.
“Fraser has done very well since coming in but we’ll have to see how that situation develops now Steve Harper’s got a bad injury.
“He’s on loan from Newcastle and we’ll have to look at that in January. If he is called back by Newcastle there might not be much we can do about it and we might have to look elsewhere.
“I don’t know about Shay Given.
“I would have to speak to (Celtic chief executive) Peter (Lawwell) about that.”