"He brought in James Harden, Omer Asik, Jeremy Lin, and Patrick Beverley. I mean it's a real good chance he wins Executive of the Year."
Morey made the blockbuster trade with Oklahoma City that brought Harden to Houston in October.
He signed Asik and Lin as free agents during the offseason and added Beverley in January as a free agent from Russia.
The NBA Executive of the Year award has been been handed out since the 1972-73 season.
The only member of the Rockets to win the award is the late Ray Patterson following the 1976-1977 season.
"I think it would mean a lot to me," Alexander said. "It would mean a lot to Daryl and it would mean a lot to the organization."
Alexander confirmed he has completed a four-year extension for Morey, which is in addition to the one year he had left on his contract.
Alexander told FOX 26 Sports in March the two sides had reached a verbal agreement.
"Daryl is an integral part of the whole organization," Alexander said. "He's proved he knows what he's doing and it's hard to get general managers who are willing to take the risk and have confidence in themselves and do the right thing and that's what Daryl does."
Naturally, Alexander is disappointed his Rockets lost on Friday 103-94 to the Thunder, eliminating them from the playoffs as Oklahoma City won the best-of-seven series four games to two.
"When we were up 10 (3rd quarter) it was getting exciting," Alexander said. "I thought we had a really good chance to beat them.The game just turned real fast.
"We had a good season. We were able to add many terrific players, a superstar in James Harden, a really good center in Omer Asik and a really good point guard in Jeremy.
"And in the middle of the season we were able to add another terrific guy, Patrick Beverley."
Beverley had a phenominal rookie season, starting the final five games of the series with the Thunder, and having a huge impact on the Rockets.
"He's great," Alexander said. "When Daryl called me and said he wanted to sign this guy from Russia, who he said was the best player in Russia, the best player out there,'I said 'okay great.'
"I couldn't believe he would be this good this quickly."
To land Beverley the Rockets had to pay the maximum allowed, $500,000, to get him out of his contract in Russia.
Alexander did not hesitate when told by Morey the move was the right thing to do.
"I think in order to have a great team you have to take some risks and you have to spend money, and I figured to be a good owner you have to do those things," Alexander said. "Otherwise, you might as well not own the team.
"In order to win championships and get back into the hunt, you really have to be willing to do that."
Trading for Harden was a no-brainer.
Going after Asik was another matter entirely.
In his second season in the NBA (2011-12) Asik played limited minutes, averaging 3.1 points and 5.3 rebounds.
This season, as a starter for the first time, Asik averaged 10.1 points, 11.7 rebounds (3rd in the league), and finished sixth in voting for NBA Most Improved Player.
Morey and his staff had been after Asik for a couple of years, and when he became a restricted free agent Morey convinced Alexander to sign him.
"That was a big risk on our part, paying him $25 million over three years, for a guy who did score three points a game," Alexander said.
"They were on me all the time, that Omer is really going to be great in this league and they were right."
As for Harden, the Rockets All-Star guard exceeded Alexander's expectations.
"I knew he was a very good player because I had watched him a lot," Alexander said. "I didn't realize how good until he started playing for us, how great he is.
"What people don't remember about James is he's only 23 years old and I told him because he has the beard people think he's a lot older than he is, but he's only 23 years old."
And Alexander knows Harden is only going to get better.
"Upside is huge, right?," Alexander pointed out. "He'll get better in every facet of the game. He works on his game. He told me that he's going to go to California and work on his game all summer.
"He's going to bring the guys there to work on it. He's a very hard worker. I know that from the fact he works really hard in practice and after practice."
Alexander's Rockets are clearly headed in the right direction and he said, in Kevin McHale, they have the right coach.
"Fabulous," Alexander said. "We had all new players, and to integrate that into one season is really difficult.
"He has a great way with the people and the players. He's always honest and he never backs down, but he has no ego in that regard.
"He's just trying to do the best job and the players realize that and they know they're talking to somebody that's done it before, many times."
Alexander will once again make every effort to improve his roster this offseason and will put the trigger if and when he and Morey find the right situation.
"Definitely, 100 percent," Alexander said.
Now that the Rockets made it back to the postseason for the first time in four years, he expects his franchise to get there again next year.
"Well, I definitely think we'll be a playoff team," Alexander said. "We'll see how far we can go next year."