However, Dern insists their relationship is strictly platonic.
"We're amazing friends," she tells Us Weekly. "We're so lucky. And we're family."
"I mean, everybody's always gonna comment about whatever seems intriguing, and he's the greatest human, and one of my best friends in the world," she adds. "So I don't blame anyone for having deep curiosity about his life cause he's spectacular."
Cooper and Shayk dated from 2015 to 2019 - and share daughter Lea, two - while Dern shares two children with musician Ben Harper, to whom she was married from 2005 to 2013.