Get up to date on Arsenal transfer news, injury updates, fixtures, not restricting reports on Arsenal Ladies and share your opinions on Goonerhead
The France international had an average season for the Spanish giants last campaign, netting 17 goals in all competitions.
The Gunners have shown interest in signing Benzema, with Arsene Wenger a big admirer of the Bernabeu star.
Wenger reportedly feels the La Liga man can replace Alexis Sanchez, who continues to be linked with an Arsenal exit.
Sanchez is wanted by Manchester City and Paris St-Germain this summer.
The 28-year-old is demanding a bumper pay rise to stay at the Emirates.
Diario Gol add that Perez wants to replace Benzema with Monaco sensation Kylian Mbappe.
Mbappe, 18, had a fine season last time out, guiding Monaco to the Ligue 1 title ahead of PSG.