The England international recently suggested that he could leave the Scottish champions in the near future.
Despite expecting bids to come in for the keeper ahead of deadline day on Wednesday, Lennon is confident that Forster will be going nowhere this month.
"I've said all along that I'm pretty confident he'll be here when the window closes, as the majority of our main players will be," he told The Scotsman.
"It wouldn't surprise me if an offer were to come in. But we're not encouraging it at the moment.
"I think he's pretty happy here. I know he has got personal aims in the future. But his short-term future, anyway, is with Celtic."
Forster joined Celtic from Newcastle United in 2012 following two separate loan spells at Parkhead.