The Gunners have been tracking the Scotland international but have yet to meet Celtic’s £25m valuation of the left-back.
Lennon doesn’t know if Tierney will still be a Hoops’ player when the transfer window shuts.
The boyhood Celtic fan has not asked for a move and remains hugely popular with supporters.
But Lennon claims speculation surrounding his future is affecting the 22-year-old.
“It’s difficult for him to keep focused at the minute because he’s only human,” said the Irishman.
“We’re supporting him all we can.”
Tierney has not played in Celtic’s three Champions League qualifiers so far following a double hernia operation but is expected to be fit next month.
Whether he’s playing in the Premier League or north of the border is a question Lennon cannot answer.
“Once they are in the door, they realise the magnitude of this club, the excitement and hat coming here and enhancing their reputation can bring”
Celtic manager Neil Lennon
“There’s a lot of speculation and obviously that is going to rumble on,” he added.
“It is as it was a week ago. Two bids have come in, two bids have been rejected and that’s where we are.
“How confident am I he’ll still be a Celtic player come the end of the window?
“Well, you can never say never. You can’t predict these things.
“If there is interest in him then other clubs may come in or Arsenal may come again.”
Lennon claims that if Tierney is sold, Celtic have plans in place to replace him – and he insists the Scottish champions are still a major attraction for players despite the pulling power of the Premier League.
“We have contingency plans and have worked out other options if that worst case scenario were to happen,” said the former Leicester midfielder.
“With the English Premier League on our doorstep, we know how difficult it is to convince players to come.
“But once they are in the door, they realise the magnitude of this club, the excitement and hat coming here and enhancing their reputation can bring.”