The 25-year-old has lost his place in the first XI this season to Oleksandr Zinchenko and has only made four starts in the Premier League - coming off the bench in a further 12 games.
After failing to earn any minutes in four successive league games, Tierney was a last-minute substitute in Saturday's 4-2 win at Aston Villa, having fallen firmly down Mikel Arteta's pecking order.
Tierney remains a crucial performer for the Gunners continentally and started all six of Arsenal's Europa League group-stage games, scoring once and setting up another to help Arteta's men top Group A.
The former Celtic man penned a new long-term deal until 2026 a couple of years ago, but having been reduced to a sporadic role this season, his long-term future is now up in the air.
According to Football Insider, Newcastle are admirers of Tierney and will monitor his situation closely ahead of a possible summer swoop.
The report states that a fee of £30m may be enough to convince Arsenal to part ways with the Scotland international, whose time at the Emirates has been disrupted by injuries.
Unai Emery brought Tierney to Arsenal for a £24m fee in the summer of 2019, and the left-back has scored five goals and set up 13 more in 112 matches for the club since.
Tierney won the FA Cup and Community Shield during his first year in North London, but he has missed a further 48 games through injury, including a knee problem which required surgery midway through the 2021-22 season.
Newcastle have three recognised left-backs in their ranks in the forms of Matt Targett, Jamal Lewis and Paul Dummett, but Dan Burn has been Eddie Howe's regular performer in that role so far this season.
Targett joined permanently from Aston Villa in the summer following a successful loan spell, but the 27-year-old has not played since the turn of the year due to a heel problem.
Dummett has also been plagued by a calf injury and is out of contract at the end of the season, while Lewis is out of favour and has only played seven minutes of Premier League football this season.
A new left-back is therefore high on Howe's agenda, and the Magpies are believed to have also shortlisted Fulham's Antonee Robinson as a target, but they will have to fend off Manchester City to sign the USA international.
Newcastle succumbed to goals from Darwin Nunez and Cody Gakpo in a 2-0 defeat to Liverpool on Saturday, during which Nick Pope was given a straight red card for handball.
Neither the suspended Pope nor the cup-tied Martin Dubravka will be available for next weekend's EFL Cup final against Manchester United, leaving Howe with a goalkeeping crisis to contend with before his side's trip to Wembley.