Forster joined Celtic on a four-year contract last summer after enjoying an impressive two seasons on loan at Parkhead from Newcastle United.
He has been linked with a return to the Premier League after recent reports claimed Sunderland were considering a move for Forster to replace Simon Mignolet.
However, Lennon is not under pressure to sell the 25-year-old and is confident he can help the keeper to reclaim his place in the England squad.
"Fraser is not for sale," said Lennon.
"I've spoken to the board about him and he's a key player. We signed him on a long-term contract last year.
"We don't need to sell him and we don't want to. He's not for sale at any price. If it's up to me he definitely won't be for sale.
"I was disappointed Fraser was left out of the England squad at the end of the season because he's good enough to play for them.
"We got him into the England squad in the first place. It was with us and through his own performances he got a chance. I'm hoping he can replicate some of those displays again for us this season."
Forster has yet to make his England debut, but was included in Roy Hodgson's squad for last October's 2014 World Cup qualifiers against San Marino and Poland.