Benzema's agent has said multiple times that the French striker will stay with Real Madrid. Arsene Wenger himself said this friday that the reports placing Benzema at Arsenal are "just rumors" and yet Italian journalist Emanuele Giulianelli, who writes for FourFourTwo and FIFA Weekly among others, says that Benzema will sign for Arsenal very soon for a fee of around €50 million. The French could arrive in London to sign his contract as soon as this Sunday, per this same report.
How reliable is this report? That's the million-dollar question. It's hard to imagine Real Madrid selling Benzema for less than €65 million when they paid €35 million years ago. Benzema was unproven back then and yet Pérez decided to spend that much money on him. With Benzema being one of his favorite players, it would be strange to see Madrid selling the player.
This move would severely hurt the team's depth, so Madrid could try to sign a replacement.