Rumours in Spain this week claim the Gunners have launched a bid to sign the 29-year-old in the January transfer window.
Benzema has only managed two goals this season and missed a clear chance against Tottenham in Tuesday's 1-1 Champions League draw at the Santiago Bernabeu.
His disappointing form has led to speculation he could leave next year, despite having signed a new four-year contract in September, but his representative has made it clear he is content in the Spanish capital.
"Karim Benzema is very happy at Real Madrid," Karim Djaziri told Sky Sports News.
"He signed a contract extension last month and has absolutely no intention of leaving the club."
Benzema missed four La Liga games with a hamstring injury but scored on his return to the side in last weekend's 2-1 win at Getafe.
The defending champions host Eibar in their next outing on Sunday.