"This is false. Their home is not on the market," publicist Karynne Tencer said.
The home took more than four years to build and sits on a seven-acre lot. It was featured in Architectural Digest in 2011, and houses a professional recording studio and screening room. Its living room has a retractable skylight and views of a man-made lake on the property.
The Smiths' home was initially reported as listed at $42 million.
Rumblings about the couple's relationship arose earlier this month, when the couple pulled their investment in privately funded New Village Leadership Academy to continue homeschooling their children, Jaden and Willow.