The Gunners broke their transfer record for Mesut Ozil in the summer but will move for his former Madrid teammate Benzema in January.
"A very important Premier League club is after Karim," Le Sport 10 quotes football agent Francois Gallardo as saying.
"This club wants the transfer to happen this winter, but if this is not possible, then next summer at the latest. The offer will be around €50m (£43m)."
Benzema recently claimed that he is experiencing a difficult time in his career, but insisted that he is determined not to "give up".