The 25-year-old has been linked with a move away from the Santiago Bernabeu, as club president Florentino Perez prepares to sell a number of first-team players, in a bid to make room for two-or-three marquee signings.
With Tottenham Hotspur winger Gareth Bale believed to be atop the Spanish club's summer shortlist, Real Madrid are understood to be willing to let Benzema leave for the right price.
However, under the new stewardship of David Moyes, it's unclear whether the Premier League champions would still harbour ambitions of signing Benzema.
Either way, the Real Madrid star has made clear he has no intention of leaving La Liga and is ready to stay and fight for his place in Los Blancos side.
"No, I'm not worried at all [about competition]," he told Marca. "Of course I'm staying. I'm happy at Real Madrid and I'm not going to leave."