Benfica have been strongly linked with a bid to sign Forster, who was this week named in the England squad for the upcoming World Cup qualifiers with Moldova and Ukraine.
However, Lennon does not want to lose the 25-year-old and has insisted that Celtic have not received any offers for the former Newcastle keeper.
The Celtic manager told the Scottish Daily Mail: "Fraser's not for sale. We had no confirmed bids for him. We have actually written a letter to one club, just warning them off basically."
Celtic on Friday announced the capture of Nir Biton after the Israel Under-21 captain completed his £1million move from FC Ashdod.
Schalke striker Teemu Pukki also completed his move to Glasgow's East End on Saturday after a fee of around £3million was agreed between the clubs and he signed a four-year contract.
A left-back is also on Lennon's wanted list and a successful pursuit would take the number of summer signings Lennon has made to seven after the captures of Amido Balde, Virgil van Dijk, Derk Boerrigter and Steven Mouyokolo.
But the Celtic boss admits adding to his squad has been a frustrating process.
"We've been looking everywhere, all over the world, really - South America, Canada, places like that and sometimes it's very difficult to do deals," he said.
"Sometimes you think you're there and then the price goes up, another agent gets involved and you end up talking to three different agents. It just becomes a bit of a muddle.
"We do our business cleanly, simply and quickly, but sometimes that can't be the case. I think there's money there to spend, it's just about trying to get the right player in for the right price."