Part of the problem, the paper said after interviewing realtors hoping to land the lucrative sale, is that the newly signed member of the Los Angeles Galaxy Major League Soccer team does not want a house that would require any remodeling to fit his preferences.

And, even though his five-year deal with the Galaxy is worth an eye-popping $250 million, he hopes to find a house for less than $20 million, the paper added.

Beckham and his wife, former Spice Girl Victoria Beckham, also want a place that is not visible from the street, the paper said.

The Beckhams have returned to Europe -- he was sent off in the final minute of his current team Real Madrid's 0-0 home draw with Real Betis on Saturday -- but plan to return soon for another search, a realtor told the paper.

The Beckhams' real estate agent, Barry Peele, declined to comment to the paper, saying he had signed a "lengthy confidentiality agreement."

The median sale price of a home in Beverly Hills in December was $1.4 million, and a little lower at $1.2 million in the coastal enclave of Malibu, according to real estate tracker Dataquick.