Beckham, 35, spent four years at Madrid and won the Primera Division title in his final season before moving to the Los Angeles Galaxy in 2007.
The former England captain, who was ruled out of this summer's World Cup after suffering an Achilles injury while on loan at AC Milan in March, also spoke of his admiration for Madrid boss Mourinho.
The former Manchester United man said of the Portuguese: "I love him as a person, he's an incredible person. He was one of the first people to send me a message after I did my injury."
On who he felt deserved to win this year's prestigious FIFA Ballon d'Or award, Beckham added: "David Villa. I think he had a great World Cup, but I'm gonna give it to Iker (Casillas, Real Madrid goalkeeper) because he's my friend!"