The celebrity Web site said Saturday the real estate hunt, which was still ongoing, apparently began about the same time Schwarzenegger left the California governor's office.
Shriver and her real estate broker perused the penthouses and a few 3-bedroom units at The Carlyle on Wilshire, a tony West Los Angeles building that is home to celebrities including Bruce Willis, Donna Summer and Dodgers slugger Matt Kemp.
Penthouses at The Carlyle sell for $10 million to $14 million, and the 3-bedrooms can be had for as low as $4 million.
Sources said Shriver decided the building was too close to the Hollywood paparazzi and was still looking for a place.
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