The Houston Rockets have major decisions to make this offseason, especially if the latest reports from Vincent Goodwill of Yahoo Sports are true.

According to Goodwill, the dynamic between Rockets stars James Harden and Chris Paul has become "unsalvageable" after a difficult season in Houston.

The relationship reportedly reached the point where Paul demanded a trade and Harden issued a "him or me" ultimatum after the Rockets' second-round loss to the Golden State Warriors.

New story: Sources tell @YahooSports Chris Paul wants out of Houston. Relationship with James Harden deemed "unsalvageable": https://t.co/UhHo0gAr8ipic.twitter.com/Txjtrvkeoc — Vincent Goodwill (@VinceGoodwill) June 18, 2019

Rockets general manager Daryl Morey has refuted the report and says Paul will be on the Rockets' roster next season, according to the Houston Chronicle's Jonathan Feigen. Morey told the newspaper he, Harden and Paul have spoken extensively about the team's plans in free agency, including getting the star duo's input on a variety of potential names the Rockets might target.

“It’s definitely not true,” Morey told the Houston Chronicle. “It’s ridiculous.”

When asked if Paul or any of his representatives have sought a trade, Morey told the newspaper: “No. Can you convey my disdain in my ‘no.’ It’s so annoying at this point.

“I’ve talked to Chris since (they were eliminated by the Warriors), for sure. Myself, Mike D’Antoni, James Harden are all super competitive, all frustrated we were eliminated from the playoffs, all want to get over the hump. That leads to a lot of competitive fire. All of it is normal. We’re all in the same boat, pursuing the championship. We’re all frustrated we’re not there. But there is nothing past that.”

That was followed by another on-the-record comment to ESPN's Zach Lowe, reconfirming the denial of a trade request. "Tweet that I said that. Print it. Tweet it twice," Morey said to Lowe.

Just spoke to Daryl Morey. He reiterated there has been no trade demand from Chris Paul. "Tweet that I said that. Print it. Tweet it twice." https://t.co/oo6ge0Wkop — Zach Lowe (@ZachLowe_NBA) June 19, 2019

Paul responded to the news on Instagram, writing "Damn! That's news to me..." in the comments of a post from Bleacher Report.

Here's more from Goodwill on the reported problems in Houston:

The backcourt mates went nearly two months without speaking to each other during the season, sources said, creating a tenuous environment for teammates and everyone involved with the franchise. Harden hasn’t returned Paul’s repeated attempts at communicating this offseason, sources said, after a year in which the pair repeatedly got under each other’s skin with petty acts in practices and games. [...] “There’s no respect at all, on either side,” a source told Yahoo Sports. “They need to get away from one another. Chris doesn’t respect James’ standing in the league, and James doesn’t respect the work Chris has put in to this point.”

Goodwill's report follows up other offseason trade rumblings surrounding Paul and the Rockets, but Morey continues to insist that both sides are in a good place.

.@SeanUnfiltered: "Does Chris Paul want to be traded?"@dmorey: "No, Chris Paul does not want to be traded."@SeanUnfiltered: "Will you field calls on Chris Paul?"@dmorey: "No, we want to add one more star to this team." — SportsTalk 790 (@SportsTalk790) June 17, 2019

Morey did not dispute the idea that Harden and Paul had a blow up after the Rockets' Game 6 loss to Golden State in the Western Conference semifinals. However, Morey told the Houston Chronicle that the interaction following that loss was a typical back-and-forth between the stars. Additonally, the Rockets have often said they challenge one another -- sometimes in an extremely pointed manner.

The Rockets were ousted in the West semifinals by the Warriors.

The Rockets GM told the Houston Chronicle he has spoken with Paul often enough in the offseason to know that Paul expects to stay in Houston and has not expressed a desire to be traded. The Rockets are expected to have only the $5.7 million mid-level exception to spend in free agency, but could seek a larger deal via sign-and-trade deals or via a trade for a potential free agent (much like Paul was when he was dealt to the Rockets in 2017).

“With both Chris and James, we’re talking about potential mid-level guys, potential top guys we might be able to trade for,” Morey told the Houston Chronicle.

“I distinctly remember one time they both face-timed me and I walked through 50 free agents and got their opinion on them together, if that gives you a sense of how tightly they are tied together.”

If the Rockets did decide to trade Paul, they may have a difficult time finding a trade partner. The 34-year old guard reportedly is due to make $38.5 million, $41.3 million and $44.2 million over the next three seasons, which would be a lot of salary for another team to absorb in a trade.

Paul -- who missed 24 regular season games due to injury -- finished the 2018-19 season with averages of 15.6 points, 8.2 assists, 4.6 rebounds and 2.0 steals.