The Gunners are said to have sought information regarding Arteta's availability, with a view to lodging a late bid.
Arsenal have struggled to match their usual free-flowing style of play following the departure of Cesc Fabregas.
Adding Arteta would go a long way towards rectifying the problem. The Everton schemer is a cerebral midfielder, with the technical quality to be a key part of the Gunners' intricate, attacking game.
Arteta is a stylish passer and is a clinical finisher in front of goal. His set-piece expertise would give Arsenal another credible option in dead situations, other than Robin van Persie.
But Arsenal's inquiries about the talented former Barcelona youth product are far from a guarantee that a deal will materialise.
Everton manager David Moyes is notorious for closely guarding his prized assets. Despite serious financial issues, Moyes will still want healthy fiscal remuneration for Arteta's services.
Wenger may not like the idea of parting with a transfer fee which is likely to exceed double figures for a player aged 29 and with a recently checkered injury record.
The Gunners boss might also feel that, after his midfield was overwhelmed by Manchester United runners on Sunday, a defensive-minded anchor man is more of a priority.
But Wenger has witnessed both Fabregas and Samir Nasri depart for pastures new this summer. A battle-tested Premier League veteran with the flair of Arteta would be a welcome addition.