According to The Athletic, Arsenal have opted not to activate an option to extend the 27-year-old’s contract.
With Tierney’s deal set to expire in June, the club could have prolonged it by 12 months.
The Scotland international is now free to sign a pre-contract agreement with non-English clubs from January 1 and could even secure a permanent transfer as soon as next month.
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A potential return to Celtic has been heavily mooted for some time, however the defender’s six-figure weekly wage – reportedly in excess of £120,000 - could prove problematic.
There has been interest from English clubs with a move abroad also possible following a loan spell at Real Sociedad in 2023/24.
Tierney joined the Gunners in 2019 but has fallen down the pecking order under Mikel Arteta and has been hit by injuries.
After suffering a hamstring injury in Scotland’s 1-1 draw with Switzerland at Euro 2024 in June, the full-back spent six months on the sidelines for Arsenal.
He returned to action in Wednesday night’s EFL Cup quarter-final against Crystal Palace and was substituted after 69 minutes of the 3-2 win.
Brendan Rodgers could look to strengthen the left-back area in the January window given the uncertainty of Greg Taylor and Alex Valle's futures.
Taylor is yet to extend his stay at Celtic Park despite his contract running down, while Valle – with whom Taylor shares the left-back position – is on a year-long loan from Barcelona with no option to buy.