However, the Hoops boss is concerned that the player won’t be fully focused now his potential Gunners switch has fallen through.
Tierney has been a key target of Unai Emery’s this summer.
But cash-strapped Arsenal are penny pinching at present, trying to preserve as much of their summer budget as possible.
For that reason, the Gunners weren’t prepared to meet Celtic’s £30m valuation of Tierney.
And Lennon now admits talks look to have ended.
“The deal, as far as I’m aware, is not happening. We are delighted about that, obviously, and it’s just a question of appeasing his mind now,” he said.
“As far as I am aware, it is finished.
“I don’t know if Arsenal are going to meet our valuation. So, it is basically, ‘As you were’.
“That may be difficult for Kieran to get his head around, or he comes back to the fold and gets on with things.
“I’ll have to speak to him about it and I’m sure the club will as well.
“But it may rumble on as well, I don’t know.”
Tierney was keen to move to the Emirates this summer.
And Lennon will be hoping the Celtic captain can get his head back in the game as soon as possible.
As for Arsenal, they will undoubtedly look for alternative options at full-back.
Speaking after this morning’s defeat to Real Madrid, Emery confirmed he was still looking to improve his defence.
“We need to improve defensively but with no loss offensively, because the first idea we developed with this team is to be offensive,” he said.
“Sometimes it’s true that we struggled defensively and to take the balance.
“Sometimes we took this balance last year and our challenge is to keep producing that.
“And with other teams we know, we are realistic, at the moment Manchester City and Liverpool they are very strong, but we want to do our way.
“To be in the top four is the same difficulty because Tottenham is growing up, Chelsea also kept their players and can keep the performance.
“Manchester United were behind us last year but they have a lot of potential as a team.”