The Frenchman is known to be keen on bolstering his central options, and has made doing so a priority for the next transfer window.
Bender was a rumoured target for the Gunners last year, but they eventually failed to lure him to the Emirates Stadium despite having scouted him extensively.
However they have remained keen on the German international, who is seen as an eventual successor to Arteta.
At 31, the Spanish midfielder is now entering the final years of his career, and Wenger is anxious to snap up an alternative to keep his side competing at the top end of the Premier League.
Bayer value their man highly, but a serious offer could be too tempting to resist this summer.
Southampton’s Morgan Schneiderlin and Ilkay Gundogan of Borussia Dortmund are also targets, but it is thought that Bender is Wenger’s preferred choice.
A new right-back is also on the agenda, with Bacary Sagna looking likely to leave when his contract expires.
Callum Chambers of Southampton has been suggested after an impressive breakthrough into the Saints’ first-team.