The defender has been heavily tipped to join Arsenal after attracting attention with a string of impressive performances for club and country.
The Gunners had a £20m offer for Tierney rejected by the Sottish Premiership champions last week.
Crystal Palace convinced Manchester United to spend £50m on their right-back Aaron Wan-Bissaka earlier this summer.
And it seems Lennon feels that Tierney, who has 12 Scotland caps under his belt, is being undervalued by Arsenal.
“I have taken no notice of the headlines,” he said. “I am well aware of where we are in terms of the situation.
“I spoke to Kieran in Austria and to be honest I haven’t really seen much of him because he came back early for rehab, so has not been on the training ground as yet.
“It can be an unsettling period for any player and that is understandable.
“But until a club comes up with any sort of realistic valuation of the player we don’t have to do anything and we won’t.
“It’s as you were. Kieran is getting on with his rehabilitation and we are getting on with what we have to do here.”
Serie A side Napoli are also interested in the 22-year-old left-back.
Carlo Ancelotti’s side can offer Tierney Champions League football – something which the Gunners cannot.
Arsenal are, however, on the verge of making their second signing of the summer transfer window.
William Saliba is set to move to the Emirates from Saint-Etienne for a fee of around £27m.
But Emery will have to wait 12 months to use him in his line-up.
The French side have negotiated that Saliba will return on loan for a year after the deal is completed.