It was reported that the France international had interested Arsene Wenger, who has seemingly admitted defeat in his pursuit of Liverpool forward Luis Suarez.
However, there has been no offer from the Premier League club according to agent Karim Djaziri who says Benzema will remain at the Bernabeu.
"We can't stop the rumours. But I tell you: Karim will not go to Arsenal," Djaziri told Le Journal du Dimanche.
"It's never been a question for him and no contact has been made."
Djaziri also believes Benzema can play a crucial role for Real this season, alongside Cristiano Ronaldo and potentially Gareth Bale.
The Welshman is believed to be on the verge of a move to the Liga side and Djaziri feels the trio would make a potent forward line.
"The probable arrival of Gareth Bale at Real Madrid doesn't threaten him at all," Djaziri continued. "Cristiano Ronaldo and Bale will play on the wings and Karim in the centre.
"Karim could very well finish his career at Real, the club of his dreams."
Benzema was on the scoresheet in last weekend's 2-1 win over Real Betis, with Carlo Ancelotti's side due to face Granada on Monday.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.