The Scotland international has been heavily linked with a move to the north London side in the summer transfer window.
The Gunners are thought to have made a number of bids ranging from £15m to £25m to sign the 22-year-old.
However, the Scottish Premier League champions haven’t been tempted into selling one of their prized assets – yet.
Arsenal’s last bid was thought to have been around £25m but was comprised of a series of add-ons.
Celtic, though, are looking to for more cash up front rather than the inclusion of incentives.
But Hoops boss Lennon was tight-lipped on talk of Arsenal’s reported £25m bid, adding that Celtic have no plans to cash in on Tierney this summer.
“It’s as you were really,” Lennon told the Daily Mirror.
“I’ve had no information other than there were two bids that came in from Arsenal that were rejected.
“There has been no further inroads into that really.
“We’re in a good position. We have got no intentions of selling, he’s on a long-term contract and we want him to progress with us.
“Our valuation of Kieran wasn’t met and it’s as simple as that.
“You will see other transfers not going through because valuations haven’t been met. It’s not a case of Arsenal being disrespectful.
“They put a bid in that they valued the player at. They came back again and obviously see Kieran as a very good player as we do.
“But on a long-term contract, we’re in a very strong position when it comes to Kieran.”
Arsenal have endured a largely frustrating transfer window so far.
Unai Emery has been linked with a host of names this summer but the Arsenal boss has only been able to get one deal over the line.
The Gunners recruited Brazilian teenager Gabriel Martinelli from South American outfit Ituano earlier this month.
Arsenal finished in fifth place in the Premier League last term and lost 4-1 to Chelsea FC in the Europa League final.
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