Spanish website defensacentral.com reports that Perez wants the former Manchester United star to become a club ambassador Stateside.
Beckham spent four years with Los Blancos before moving to the LA Galaxy in 2007 - a transfer which made him a household name in America.
It is understood that Perez is keen to tap into Beckham's fame in the US and help make them the biggest club across the pond.
Real have already signed up club legends Ronaldo and Roberto Carlos to act as ambassadors and are currently in talks to have Raul join in a similar role.
But Beckham is the one they want as the Spanish giants look to make a splash in the United States market in the near future.