The 22-year-old has been strongly linked with a move to The Emirates this summer as Unai Emery looks to try and bolster his options on the left side of defence.
Lennon has now confirmed that Celtic have rejected two bids for Tierney so far this summer, and it remains to be seen whether Arsenal will return with another bid to try and sign him before Thursday’s transfer deadline.
The Celtic boss, however, has been delighted by the way the Scotland international has been been handling the situation about his future in recent weeks.
Speaking in an interview quoted by Sky Sports, Lennon said: “Obviously the window in England shuts on Thursday.
“It can be an unsettling period for any player. We have rejected two bids and the clubs know the valuation that we value Kieran [Tierney] at and it’s not been met.
“He is dealing with it very well. We are living in an age now where it’s coming at you from all angles, especially on social media.
“He is only 22. We have to be mindful of that as well. He is trying to keep his feet on the ground and stay focused on the present.”
Arsenal completed the club-record signing of winger Nicolas Pepe from Lille last week.
The north London side have also tied up deals for William Saliba, Gabriel Martinelli and Dani Ceballos on loan from Real Madrid.
Arsenal have not won the Premier League title since 2004 and they will kick of their top-flight campaign when they take on Newcastle United at St James Park on Sunday 11 August.
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