The French ace has just moved to Los Merengues from Lyon on a six-year deal for €35 million, and he was officially unveiled on Thursday.
However, Benzema hasn't been given a Jersey number yet, and the 21-year-old hopes for the number 10.
"I like number 10, but I'll have to wait for some shirt numbers to be free," the international hitman told Real's official website.
From his side, Real general director Jorge Valdano said: "Karim doesn't have a number yet because they are all taken.
"He felt it was disrespectful to wear another team-mate's number. The club also thought it would have been unethical to give him the shirt number of a player that is still with us."
Real's squad includes 35 players, therefore they must offload at least 10 men in the close season.
Dutch midfielder Wesley Sneijder is currently wearing the number 10.
The 25-year-old said last month that he has no plans of leaving Real this summer.
But The Spanish giants are likely to sell him in the close season, especially after completing the signing of Cristiano Ronaldo from Manchester United.
Renowned Spanish paper Marca suggest that Real's old guard are planning to stay put, although they don't have a chance of retaining their regular spots next season.
Real chairman Florentino Perez is aiming to comprehensively dismantle the squad by bringing in a host of superstars and getting rid of the players who joined the club during Ramon Calderon's tenure.
Marca pointed out that those who are determined not to leave Manuel Pellegrini's side are well-paid at the capital club, and won't be able to secure similar wages elsewhere.