Nevertheless, Kevin’s representatives were quick to quash the story.
They told MailOnline: “The rumour regarding Mr Costner impregnating a woman on the set of Yellowstone is absolutely not true and is defamatory.”
Kevin and Christine married in 2004 after meeting on a golf course in the late 1990s.
Their wedding was a lavish affair complete with a horse-drawn carriage on his Aspen ranch. They went on to have three children: Cayden, 15, Hayes, 14, and Grace, 12.
Although Yellowstone will be wrapping up with the upcoming second half of season five, an untitled sequel is in the works.
It is expected to come out in December and reports have said Matthew McConaughey could be attached to the project.
“Yellowstone has been the cornerstone on which we have launched an entire universe of global hits – from 1883 to Tulsa King.
“I am confident our Yellowstone sequel will be another big hit, thanks to the brilliant creative mind of Taylor Sheridan and our incredible casts who bring these shows to life,” said Chris McCarthy, President & CEO Showtime/MTV Entertainment Studios.