"They're taking a break," one insider told the celebrity news website.
Word the couple have been spending time apart the past few months comes after Douglas, 68, recently battled throat cancer and Zeta-Jones, 43, was treated for bipolar II disorder.
"The stress has taken a toll on their marriage," a second source told People.com.
Neither star has officially filed for divorce or legal separation, the report said.
The couple are the parents of Dylan, 13, and Carys, 10.