"You have to know there are just so many outlets," he commented.
"It's better that you get out in front of it and tell your story before it becomes gossip," he said.
The actor is currently at the Cannes International Film Festival in France promoting his role as flamboyant musician Liberace in HBO film Behind The Candelabra.
After battling throat cancer, he was thrilled to be given this part in particular.
"I was just happy to be alive, and then someone hands me one of the best scripts I've ever read," he said.
"Steven Soderbergh tells me he's going to direct, Jerry Weintraub is going to produce, Matt Damon is going to be my co-star and I get to play Liberace!"
He says it was almost "too good to be true," but admits he was ready for some good luck.
Douglas, 68, is confident that his health will be back on good form for a while now.
He is looking forward to the future with Zeta-Jones, 43, plus their son Dylan, 12, and daughter Carys, nine.
"I feel great. I'm cancer-free, and with my particular type of cancer, if you're free after two years, it doesn't usually come back," he said.
- Cover Media