The north London club have been heavily linked with a move to bring the Scotland international to The Emirates as Unai Emery looks to strengthen his options at left-back.
According to Sky Sports, Arsenal have already had two bids for Tierney rejected by the Scottish club – but recent reports suggest that the Gunners have not given up hope of signing him.
Now, Lennon has delivered an update on Celtic’s position amid the speculation about Tierney’s future this summer.
Speaking in an interview quoted by Sky Sports, Lennon said: “There is a lot of speculation – that is going to rumble on – and I am sort of at ad nauseam of answering the same questions over and over at every press conference.
“It is as you were a week ago. Two bids have been in and two bids have been rejected. That is where we are.
“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 is working away in the background and it is difficult for him to keep focused at times because he is only human. But we are supporting him all we can.”
Arsenal are currently preparing for Unai Emery’s second season in charge of the north London club.
The Gunners finished in fifth place in the Premier League table and without a trophy last term after they lost the Europa League final to Chelsea FC.
After having signed Brazilian teenager Gabriel Martinelli, Arsenal confirmed the loan arrival of Dani Ceballos and the signing of William Saliba, who will return to Saint-Etienne on loan, last week.
Arsenal have not won the Premier League title since their famous unbeaten triumph in the 2003-04 campaign.
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