However, the 25-year-old’s agent Karim Djaziri insists Benzema, who scored 11 goals in 30 top-flight appearances last season, wants to stay in the Spanish capital.
“Nothing has changed,” Djaziri told BBC Sport. “Karim isn’t joining Arsenal or anybody else. He’s staying at Real Madrid.
“In any case, he’s joined up with the France team today, and I doubt they’d even allow him to leave to discuss a move.”
Benzema has struggled to win over the Real Madrid supporters following his €41m (£35m) move to the Bernabéu from French side Lyon in 2011.
Madrid manager Carlo Ancelotti hinted Benzema’s attitude hasn’t helped the striker win over the club’s fans following a 3-1 victory over Athletic Bilbao on Sunday.
“Today one thing was very clear. Benzema was whistled a bit, while Di Maria was applauded by whole stadium,” Ancelotti told reporters.
“The fans look closely at the players. It’s a very clear sign for everyone that hard work is applauded.”
Get enhanced odds of 18/1 on Andy Murray to win Wimbledon or 10/1 on Novak Djokovic when you open a Paddy Power account.