The Scotland international was one of the Gunners’ top performers last term, registering two goals and five assists from 38 appearances.
The left-back has become a firm favourite among the fans, and the club are now keen to secure his long-term future with an improved deal.
Tierney has three years remaining on his contract, but the hierarchy are prepared to reward him for his impressive performances.
Tierney had an injury-plagued debut campaign for the Gunners in 2019/2020, but had a much-improved fitness record last season.
He still missed 11 league games due to injuries, and the club are lining up a young player, who can provide quality back-up to the Scot.
Aside from his goal contributions, he impressed with regular overlapping runs last term, and was the most creative full-back in the squad.
Calum Chambers complemented him impressively in the opposite end in the final months, and they could be the regular full-back pairing.
The Gunners are still on the search for another right-back, and they have recently been linked with a move for Lille’s Zeki Celik.
Tierney, who is valued at £28.8 million by Transfermarkt, is expected to start for Scotland in the back three at the European Championships.
The nation will begin their group stage campaign against Czech Republic on Monday.
Stats from Transfermarkt.com