AC Milan and Napoli have both been credited with an interest in the Frenchman, and it was claimed last week that the striker was nearing a switch to Milan.
However, the 30-year-old has said that he wants to "make even more history" with the European champions during the 2018-19 campaign.
"We must carry on winning titles because here the objective is to always win things together," Benzema told RMTV. "On a personal level I want to do better than last year and I need to keep working to make even more history with this club.
"I never imagined winning everything I have, but I signed for Madrid to win trophies and to be a success. I knew I was going to have some difficult times, but that doesn't matter because this is the best club in the world. I am very happy."
Benzema has scored 193 times for Madrid since a 2009 switch from Lyon, but the forward managed just 12 goals in 47 appearances during the 2017-18 season.