The Gunners have been tracking the German international for some time, and even had an £18.5m offer for his signature rebuffed by the Bundesliga giants over the summer.
But, Arsene Wenger is still keen on the holding midfielder as he plans for additions when the transfer window re-opens.
The Frenchman has made an enforcer one of his major targets despite drafting in Mathieu Flamini.
Bender is his preferred choice after a series of impressive displays both domestically and on the international stage.
The 24-year-old has been recommended to Wenger by recent arrival Mesut Ozil, who is quickly developing into a key figure at the Emirates Stadium.
Leverkusen are in no rush to sell one of the prized assets, having allowed Andre Schurrle to leave for Chelsea in a big money deal earlier this year.
But, Arsenal are hopeful that Bender will pursue a move, which may force his employers to accept a £20m offer.
Manchester United are also keen, as they search for an emerging midfielder to partner Marouane Fellaini.
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