The 33-year-old has spent the last 12 years at the Santiago Bernabeu, scoring 290 goals and providing 152 assists in 570 appearances across all competitions.
Benzema has less than two years remaining on his current contract and although Los Blancos would seemingly want to extend his deal, the Frenchman has not ruled out a fresh challenge in a different league before he retires.
"I take things year by year, as long as I have this desire, this joy and I like football then I will continue," Benzema told ESPN.
"I don't look at age, it all comes down to how I feel, I will never force it, I feel better and better as I keep playing. I like the United States, soccer is getting better there."
Benzema, who has been nominated for the 2021 Ballon d'Or, has made a brilliant start to the new campaign, scoring 11 goals in as many games across all tournaments, including nine strikes in just eight La Liga matches. body check tags ::