Shams Charania of The Athletic and Stadium reported the Rockets had "preliminary conversations" with teams about Paul and have also shopped center Clint Capela. The discussions surrounding Paul were largely around finding a team willing to absorb the final three years of his contract.
It does not appear any of those talks have gained traction.
Morey appeared on SportsTalk 790 earlier Monday and tried to put the Paul trade rumors to bed.
Paul has spent the last two years in Houston, both of which ended with the Rockets being eliminated by the Golden State Warriors. ESPN's Tim MacMahon reported tensions boiled over between Paul and James Harden following their Game 6 loss to Golden State in the conference semifinals, with Paul growing frustrated at the Rockets' lack of ball movement.
"What you have are two highly competitive guys who were very disappointed that we didn't beat Golden State," Morey said. "You've got two high-level competitors who want to figure out how to win at a higher level, as well. Naturally, people who want that so bad, something that's so tough, it's going to create sometimes things that need to be discussed. But it's all, to me, in bounds of any superstars."
The Rockets averaged 22.4 isolation possessions per game during the regular season. No other team had more than 10.5.
Given the unlikelihood of the Rockets finding a taker for Paul's contract, the likes of Capela, Eric Gordon and PJ Tucker are more available to trade.
Capela is arguably the Rockets' best trade piece, a 25-year-old center who averaged 16.6 points, 12.7 rebounds and 1.5 blocks per game. He's also on a relatively team-friendly contract, negotiated last summer when he was a restricted free agent. If Morey is looking to find a third "star" to add to the puzzle, the conversation will likely begin with Capela.