The couple recently paid $11 million for a 10,000-square-foot mansion in a gated community and have already had the house gutted for renovation to a 14,000-square-foot design, TMZ.com reported Tuesday.
Us Weekly reported afterward it had independently confirmed the purchase and added that reality star Kardashian, 32, and rapper-producer West, 35, had looked at the property Jan. 2.
The renovation will convert the house to an Italianate villa, TMZ said, with amenities such as a gym, movie theater, bowling alley, basketball court and indoor and outdoor pools.
West revealed girlfriend Kardashian's pregnancy during a concert in Atlantic City Dec. 30.
Kardashian filed for divorce on Oct. 31, 2011, just 72 days after a lavish wedding that became the basis of a TV special. In 2004, she divorced music producer Damon Thomas after four years of marriage.
West on Monday tweeted a photo of himself and Kardashian sitting next to singer Beyoncé and her husband, rapper-producer Jay-Z, with the caption "FAM," leading to online speculation that Kardashian and West may name them as godparents.