Speculation that the Gunners will move for the France international has been going on all season but the recent comments of Gunners director Lord Harris has seen them intensify.
Harris suggested that Arsenal were in a position to buy any player in the world - bar Cristiano Ronaldo or Lionel Messi - and that the club were ready to break their own transfer record which stands at £42.7m, which they paid Real Madrid for Mesut Ozil.
Following Real Madrid's victory over Manchester City, Benitez was asked about the rumours. The former Liverpool boss began by saying he refuses to talk about players at other clubs, and that he wasn't keen to talk about his own.
"In this case - Karim is our player," he said. "I hope, I'm sure he will stay with us."
Benzema has been at Real Madrid since 2009 during which time he has scored 87 goals in 188 La Liga appearances.
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