"He's the cornerstone of the team," Morey said.
A few days later, the future of the team and the All-Star center from China have suddenly been thrown into question amid ominous reports from the team doctor that the hairline fracture in Yao's left foot could not only possibly keep him out all of next season, but potentially end his career.
That would not only be devastating news for the Rockets, but a crippling blow to the NBA, which would lose one of its most influential international ambassadors.
On Tuesday, the league was still holding out hope that Yao would play again.
"I think it's awfully premature for us to comment on that," league spokesman Tim Frank said. "Let's see how this works out first."
Morey said Monday he would not comment on the reports about Yao "until we have all the facts." A team spokesman said Tuesday that nothing was definitive and that Yao and his representatives were seeking other medical opinions this week.
The Rockets already know that Tracy McGrady could be out until next February after undergoing risky microfracture surgery on his left knee. Morey also has to decide what to do with Ron Artest, who becomes a free agent after making over $7 million in a productive first season in Houston. Artest said after the season that he wanted to come back -- but that was when he believed the Rockets could compete for the Western Conference title.
Releasing McGrady and Artest could save the Rockets money, but probably cost them a season. It would also mark a disappointing end to the star-crossed pairing of Yao and McGrady.
The two have only played together in 220 games across five seasons. Together, they've missed 204 games to injuries and illnesses since McGrady joined the team in June 2004.
Yao and McGrady have played in 10 All-Star Games as Rockets, but they've never led Houston out of the first round of the playoffs together. McGrady watched from the sidelines as Houston beat Portland in the first round last season, the Rockets' first series victory since 1997.
Yao was injured in Game 3 of the second-round series with the Los Angeles Lakers, and Houston pushed the eventual NBA champions to seven games. But the scrappiness the Rockets showed won't be enough to carry them through a whole season without a superstar.
That leaves Morey with difficult -- and far-reaching -- decisions to make this summer.
Yao is due to make over $16 million next season, with a player option for 2010-11 that would pay him over $17 million. McGrady will make over $22 million next season, the last year of his contract.
Before the draft, Morey said teams have made "very aggressive" offers for McGrady. They're probably more interested in McGrady's expiring contract than what he could provide on the court, but either way, Morey hasn't seen a deal he likes.
"We are getting a lot of interest on Tracy and I do have to listen," Morey said. "It's my job to make this team as ready to win the title as possible."
But how realistic is that if Yao is sidelined for the season or longer?
Morey said last Friday that the uncertainty surrounding Yao had not changed his offseason strategy for trades. That was before team doctor Tom Clanton told the Houston Chronicle that Yao's injury could threaten his career.
If Yao is out for the season, the Rockets could apply for an injured player exception and use that money toward signing a free agent, said Frank, the NBA spokesman. It would amount to the value of the midlevel exception, equal to 108 percent of the average player salary from last season (about $5.6 million).
Some of the unrestricted free agent big men available this summer, if the Rockets won't have Yao, include Chris Andersen, Brandon Bass, Rasheed Wallace, Antonio McDyess, Chris Mihm, Francisco Elson, Jamaal Magliore and Drew Gooden.
A doctor approved by the NBA would have to declare Yao out for the season before Houston would get the exception. And the Rockets would not be able to combine the two exceptions to make an $11 million offer to one player.
The absence of Yao would have a major impact far beyond Houston.
Rockets games routinely draw television audiences between 20 and 30 million in China, said Marc Ganis, the president of the Chicago-based sports consulting firm SportsCorp Ltd., which has partners in China.
The NBA became the first American sports league to host games in China in 2004, when Yao's Rockets played Sacramento in Beijing and Shanghai. The league opened offices in China in January 2008, and NBA games and programming are available on 51 television and digital outlets there.
Ganis says the NBA would've eventually developed a strong presence in China, but Yao accelerated the process by a decade or more. Yao adorns larger-than-life billboards, stars in commercials and even provided the voice for a character in a Chinese-language animated movie after the Rockets' season.
"His emergence as a rock star allowed the NBA to get on his broad shoulders and be carried to a much higher level of popularity than it would've been," Ganis said. "His value to the league has been almost incalculable."
Even if Yao never plays another NBA game, Ganis said his international impact is permanent.
NBA merchandise is sold in 30,000 retail stores in China. Kobe Bryant has had the top-selling NBA jersey in China for two straight seasons. Yao ranks 10th, but only because most Chinese fans already have them.
"It's inevitable that one day, he will no longer be playing in the NBA, but that could be a decade down the road," Ganis said. "But I would expect Yao to be an ambassador for the NBA in Asia and I would expect him to be a significant contributor for the development of basketball in China."
For now, all China, the Rockets and everyone else can do is wait to see if he plays in the league again.