The Gunners are keen to lure the 22-year-old to the Emirates this summer.
Tierney has emerged as a top target in north London, with two bids having already been rejected at Celtic Park.
Arsenal have failed with £15m and £18m approaches for the young Scotland skipper so far.
Celtic are said to be holding out for £25m for their top talent and Unai Emery’s side are still searching for an agreement.
Tierney would be in line for a mega pay rise if he chose to ply his trade in England’s top flight too.
A £70,000-a-week contract over the next five years is reportedly being proposed by Arsenal.
And amid the claims surrounding Tierney’s future, transfer expert Ian McGarry has suggested Champions League winner Robertson has held talks with the player.
The two Scotland left-backs know each other well from their time together at international level.
“Lot of rubbish”
And McGarry has claimed Robertson has looked to push Tierney out the door at Celtic, having said: “The second thing that has changed for Kieran Tierney is speaking to his international teammate Andy Robertson.”
The rumour did not go down well with some Liverpool fans as the move would certainly strengthen Arsenal’s cause next season.
However, Robertson has insisted he has nothing to do with the proposed transfer, tweeting: “Lot of rubbish”.
Robertson was keen to distance himself from the link given he is a boyhood Celtic supporter.
Tierney is too and will want to tree carefully over his future in order to keep his relationship with the club on good terms, even if he does go.
Arsenal need a long-term solution at left-back given Nacho Monreal’s time at the club is coming to an end.
Tierney has shown he is ready for the step up having already gained good experience in the Champions League and at international level.
He also offers Arsenal versatility as a possible option on the left of a three-man defence.