The Gunners have been unsuccessful in their summer-long pursuit of the 22-year-old, and have been left frustrated despite lodging two separate bids – the second of which was for £25 million ($31m).
So far, the Scottish champions have held firm over their valuation of the left-back, but Hoops manager Lennon has not ruled out another bid from the north Londoners before the August 8 deadline.
Speaking to the press ahead of Celtic’s season opener at home to St Johnstone this Saturday, he said: “Normally these things tend to happen again so it would not surprise me, put it that way.
“That’s not from personal knowledge of anything, that’s just my own experience of things.
“We know the window shuts on Thursday, so if we are talking about Arsenal then they have five or six days to come back with a revised offer.”
Scottish international Tierney, who has 12 caps for his country, is currently recovering from a double hernia operation but is hopeful of a return to full-fitness soon.
And transfer talk aside, Lennon freely admits that getting the fan-favourite back up to speed in training has been one of his top priorities.
“We will continue on and get Kieran back with us and fit as quickly as possible because he is such an important player,” he said.
Despite making Nicolas Pepe his third signing of the summer on Thursday, following deals for William Saliba and Daniel Ceballos, Gunners boss Unai Emery is thought to be keen to bolster his back-line before the big kick-off.
Celtic, meanwhile, will not make any new signings before the Champions League third qualifying round tie against Cluj.
However Lennon believes his squad is more than ready to launch their bid for what would be a record-equalling ninth-successive Scottish league title.
“They don't really talk about it (nine in a row),” he said. "That’s for fans and media, it gives them something to talk about.
“We've asked the players whether it’s your first, fifth, seventh or ninth title, have you got the hunger to go again? You can see it in their eyes, they're well set to go.”