The Scotland full-back joined the Gunners in the summer of 2019, but has been limited to just 87 appearances in that time with injuries stopping him from featuring on a more regular basis.
Making just 22 Premier League appearances last term, the 25-year-old missed the end of the campaign after undergoing knee surgery with the player being eased back into action during pre-season.
With concerns over his long-term fitness, former Arsenal and England physio Gary Lewin believes that he wouldn't be surprised if the Gunners were looking at other options, with Oleksandr Zinchenko close to joining the club.
Speaking on White and Jordan, Lewin said: "it's a combination of a lot of things, really.
"You can't say that the Scottish Premiership isn't physical, so you think he'd adjust quite quickly so I think it's adjusting to a new team, a new way of training, a new style and a lot of players do get that.
"Regarding the 30 minutes that he played last week, I think that was pre-planned because you're better off with a player who is going to play 30 and bringing them on, because things change in a game and you might end up playing more than you want to.
"All clubs are doing the same thing at the moment. They're individually planning players' pre-season return to play and I think you'll see a lot of this during the whole of the pre-season training."
Asked if Arsenal will target a replacement for Tierney as a result of his injuries, Lewin said: "Clubs are continually assessing what they've got and there will be medical involvement, but ultimately it's a football decision.
"All clubs will strengthen in areas where they think they need strengthening.
"Last year Arsenal had the issue that when Tierney was injured, they had to fill the left position with players out of position, so I don't think it's a complete surprise that they're looking to strengthen that, but I think you could argue that across all clubs.
"They'll be looking to strengthen and tweak their squad across the whole pre-season and transfer window."