The France star has been linked with a move away from the Bernabeu in recent months.
Benzema, 29, has struggled to impress this season under Zinedine Zidane.
The striker has netted four goals in 15 appearances for the Spanish giants this time out.
And according to Spanish news outlet Diario Gol, Arsenal have tabled an offer for the Real hitman.
They claim Arsene Wenger is a huge admirer of the striker and would love to have the Frenchman at the Emirates.
However, Diario Gol add that the Gunners are not willing to pay more than ZAR723.93 m for Benzema.
Zidane has reportedly given the green light for Benzema to leave the Bernabeu.
However, Real are keen to get at least ZAR904.91 m for Benzema.
Diario Gol also say that Real are already eyeing replacements for their striker, with club president Florentino Perez keen to sign a Galactico.