Unai Emery is keen on landing a quality left-back to the Emirates Stadium with Tierney being a priority.
The Gunners were highly reliant on their only left-backs Sead Kolasinac and Nacho Monreal this season with the latter being tipped for a summer exit.
While in Scotland, Tierney continues to be a priceless asset for the Celts.
Despite some injury setbacks, the 21-year-old managed to play 40 matches this season, providing four assists.
An academy graduate of the Hoops, Tierney has made 167 appearances overall since joining the first-team in 2014. He has also earned 12 caps for the Scotland national team.
Tierney will next play in the Scottish Cup final this week and will undergo a double Hernia operation as a result of the horror injury he suffered against Aberdeen last month.
How Tierney’s exit will affect the Hoops?
Neil Lennon, the interim manager, seems to have no feasible options other than Tierney at the moment.
Emilio Izaguirre, the second choice full-back is also on the verge of summer exit as his contract expires next month.
Read more Celtic FC News, click here – Latest Celtic FC News
The Bhoys beat Hearts 2-1 in the Scottish Cup final and completed a treble.