Tom Pelissero of NFL Network reported the news, noting Clowney is "unhappy with the state of talks about his future."
The three-time Pro Bowler is yet to report to training camp after being franchise tagged this offseason. Pelissero noted he's expected to sign his tender and report to training camp this week.
"Until he decides to come in and sign the tender, really the ball's in his court relative to playing for the Texans and all those things, just like it's been since the beginning of training camp. He's a franchise player and so until he comes and signs the tender, really there's nothing really else to talk about," Texans coach Bill O'Brien told reporters.
Clowney recorded 47 total tackles and nine sacks in 2018, his third straight Pro Bowl campaign. While he has not become the most dominant pass rusher in football the way the Texans hoped when they took him first overall in 2014, Clowney's physicality and speed off the edge have turned him into a star.
John McClain of the Houston Chronicle tweeted earlier this month he'd be "surprised" if Clowney is not traded, but no suitor has emerged. The Texans are reportedly looking for a franchise left tackle in return.
Clowney firing Cook should not be a surprise, given the botched nature of the contract talks. He will be forced to play out the franchise tag in 2019, and his continued holdout is more an illustration of displeasure with the situation than anything.