The Gunners have had a £15m bid for the defender turned down by the Scottish Premiership champions.
Boss Unai Emery feels that Tierney is the ideal left-back to replace the ageing Nacho Monreal.
Despite being just 22 years old, the Scotland international has already played 167 games for Celtic.
But Arsenal supporters are panicking because he has also missed 41 matches through injury in the last three seasons.
In the 2016/2017 Tierney missed 85 days of action after suffering a ruptured cruciate ligament.
And last term he made just 19 league appearances due to a hip injury, Cals Sclerosis and groin surgery.
“He’ll fit right in at Arsenal,” tweeted one Gooner in response to the stats posted by @MrArsenicTM on Twitter.
“Still defends better than a healthy Kolasinac,” replied another.
A third wrote: “Well a match made in heaven.”
“Looks like the perfect player for us then,” added a fourth.
But some Gunners fans were a bit more optimistic.
“He’s 22 and played over 200 games you’d expect it tbf,” one wrote in response to the negativity.
Despite having their opening bid for Tierney rejected, David Ornstein says Arsenal are confident of getting a deal over the line.
“As reported elsewhere Arsenal have had an opening bid of £15m for Celtic left-back Kieran Tierney rejected,” the BBC reporter tweeted.
“But there is optimism an agreement will be reached between the clubs.
“Personal terms for the 22-year-old Scotland international shouldn’t be a problem.”
Tierney is currently recovering from surgery to solve a niggling hip problem but should be back in time for the new season.