The Gunners had already been contemplating how to add greater depth to their defence in recent weeks, but Tuesday night's embarrassing defeat to League Two Fleetwood Town in the EFL Cup could enhance the chances of a signing.
While one result is unlikely to dictate their transfer strategy, Arsenal are continuing to assess where further reinforcements could prove valuable.
Kim, 29, is one of the names under consideration ahead of the winter window. He is contracted to Bayern until 2028 but has been in and out of the starting line-up, leaving questions over how central he will be to their plans in the months ahead.
The defender recently featured against Arsenal in the Champions League, giving the Gunners a close-up look at a player who could offer an experienced option at the back.
Bayern are not desperate to sell Kim, who has also been linked with AC Milan, and their position would depend heavily on the terms of any proposal.
A sufficiently attractive offer could open the door to negotiations, but the German champions are not expected to facilitate a departure simply for the sake of it.
That leaves Arsenal with a decision to make over how far they are prepared to go financially for the player.
Kim is not the only defender being considered, with Arsenal understood to have a variety of names under review as they weigh up their priorities for January.
The club's continued interest in adding depth suggests they are keen to avoid being caught short during the second half of the campaign.
The winter market can be difficult to navigate, particularly when pursuing established players from major European clubs. And Bayern's willingness to listen would likely depend on the value of the offer - and their own assessment of squad needs.