The ex-Malaga man thinks the Blancos skipper should try his hand away from the Santiago Bernabeu and suggested Juan Mata is bound to leave Chelsea.
Mesut Ozil jumped ship from the Santiago Bernabeu for the Emirates Stadium at the start of the season, and Cazorla, who left La Liga for England in 2012, thinks Diego Lopez's deputy at the Blancos should follow suit.
"Casillas should try playing somewhere else," the ex-Villarreal and Malaga star said of his Spain teammate to beIn Sport. "I learn from Ozil every day; having him with us at Arsenal is a great opportunity."
The 29-year-old also mused that Chelsea winger Juan Mata, another Spaniard who is struggling to get regular game-time, will depart Stamford Bridge in 2014 at this rate.
"If Mata doesn't play he will want to leave Chelsea, that's obvious," Cazorla said.
Cazorla scored both of the Gunners' goals as they defeated relegation-threatened Fulham 2-0 on Saturday to ensure they stay top of the Premier League with 22 games gone.