France international Benzema has been at the Santiago Bernabeu since joining from Lyon in 2009 but he was linked with a move away from the Spanish giants in the recent summer transfer window.
Premier League outfit Arsenal were believed to be showing a keen interest and it was thought the striker would relish the opportunity to challenge compatriot Alexandre Lacazette for a starting berth at the Emirates.
However, when asked about his future at Los Blancos, the 29-year-old revealed he is more than happy at the club and feels a move away would represent a backward step in his career.
"It is the best club in the world," Benzema told BeIn Sport France. "It is a pleasure and makes me proud. The expectations are very big and every season you start from scratch. You have to work to keep yourself at the highest level.
"If you are a starter here, you do not need to go elsewhere. I think we are in one of the best stages of Real Madrid's history. The team is very strong, it's not just a matter of those who are usually the starters; the substitutes also make a difference."