The former French international has been in top goal scoring form for Zinedine Zidane's side this season, registering 12 La Liga goals in 19 appearances.
According to AS, Benzema has been in talks about a new deal since December, with both parties said to be happy with the Frenchman extending his stay at the club.
The 32-year-old joined Real Madrid from Lyon in 2009 and has now scored 238 goals for the club.
Despite being in the latter years of his career, Benzema had the third best goal scoring season of his career last term and is said to have impressed the club's hierarchy with his new fitness regime. body check tags ::