Tierney has made just four starts in the Premier League under Mikel Arteta this season.
Summer signing Oleksandr Zinchenko has cemented the left back spot as his own as the Gunners look to secure their first Premier League title in almost two decades.
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Newcastle are determined to secure the signing of an experienced player in the left back position this summer, with Eddie Howe a long-term admirer of the Scotland international.
Howe attempted to sign Tierney when he was manager of Bournemouth in 2018 and has kept tabs on his progress since he was a youngster at Celtic.
LondonWorld understands Tierney remains focused on the current campaign with Arsenal and increased game time appears likely next season with Mikel Arteta’s side set to qualify for the Champions League.
“I’ve not started many games,” Tierney told The Scottish Sun in January.
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“But there’s also only a few games where I’ve not come on. “It’s a long season and it’s not just 11 players needed, it’s the full squad.
“There are different ways you can vent your disappointment. One way is to not try and openly show you don’t care.
“But there’s another way — you work hard and give your all for the team, you try to push as much as you can and, when called upon, you give everything. And that’s the way I choose.”