The English Premier League club have had two bids, the second an instalment-based offer in the region of £25m, rejected for the 22-year-old left-back.

Lennon reiterated he is not aware of any resumption in talks with Arsenal.

"We obviously have worked out other options if that worst-case scenario were to happen," Lennon said.

Celtic have already signed one left-back this summer, with Belgian Boli Bolingoli arriving from Rapid Vienna.

England's transfer deadline is 8 August - three weeks before the Scottish window closes.

"It is as we were a week ago," Lennon said. "Two bids have been 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. Having that extra two or three weeks later on in the window may be beneficial."

Italian Serie A club Napoli, who face Liverpool in a sold-out friendly at Edinburgh's Murrayfield Stadium on Sunday, have also been credited with interest in Tierney this summer.

Lennon says the Scotland international, who has not appeared in Celtic's Champions League qualifiers as he continues his recovery from a double hernia operation, has been affected by "a lot of speculation".

"That's going to rumble on," he suggested. "If there is interest in him then other clubs may come in or Arsenal may come again. I can't predict that.

"At the minute, he's working away in the background and it's difficult for him to keep focused at the minute because he's only human, but we're supporting him all we can."