The Frenchman has been linked with a move away from the Bernabeu this summer after struggling for form.
He has netted just nine goals in La Liga this season, and with Real Madrid planning to land a marquee signing in the transfer window Benzema’s position at the club is under threat.
And according to Spanish publication Don Balon, Benzema has five offers on the table from clubs across Europe chasing his signature.
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Arsenal are long-term admirers of the striker having tried to sign him in previous transfer windows and reports in Spain last week suggested they were ready to offer him a contract worth £300,000 a week.
But Don Balon claim Liverpool are also interested in his services with Jurgen Klopp keen to strengthen in the summer, that could see them make a move.
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Daniel Sturridge’s future remains unclear and Klopp would be on the hunt for a replacement should the England international leave.
Benzema is also said to have Inter Milan, AC Milan and Paris Saint-Germain chasing him.
The 29-year-old remains under contract with Madrid until 2019.