The 22-year-old has struggled to cement his place in the Gunners first-team this season, and has been restricted to just three Premier League starts in 2012/13.
Arsene Wenger is understood to rate the Frenchman highly, but is unable to accommodate the player in his plans, due to the fine form of his current first-choice stars.
Jack Wilshere, Mikel Arteta, Santi Cazorla, Tomas Rosicky and Aaron Ramsey have all impressed in the Arsenal engine room, meaning regular opportunities in the starting XI have been few and far between for Coquelin.
The Bundesliga club are now looking to capitalise on the uncertainty surrounding the France U21 international's future at the Emirates Stadium, and are ready to offer him the chance of consistent action in Germany.
Coquelin has previously enjoyed temporary loan spells away from north London, and underwent a successful stint with Ligue 1 side Lorient last season.
His impressive form in his native France prompted Wenger to give the midfielder a chance to prove himself in the Premier League, but Coquelin has failed to capitalise.