Houston will not need surgery despite having sprained ligaments and torn muscles in his elbow, according to the report, which cited two sources with knowledge of the Pro Bowl linebacker's recent MRI results.
The Chiefs have officially stated that Houston, who is tied for third in the NFL with 11 sacks, suffered a dislocated elbow in last Sunday's loss to the San Diego Chargers.
Houston missed practice Wednesday and likely will not play in this Sunday's showdown with the Denver Broncos, sources told ESPN NFL Insider Adam Schefter earlier this week.
The 24-year-old Houston originally was scheduled to undergo an MRI on Monday, but the testing was postponed because of swelling in the elbow.
The Chiefs (9-2) also could be without two-time Pro Bowl linebacker Tamba Hali for their rematch with the AFC West rival Broncos (9-2), who have the league's top-ranked offense.
Hali, who suffered a slight ankle sprain against San Diego, also missed Wednesday's practice but insisted he will play Sunday against Denver.
"I'll be ready to go," Hali said Wednesday. "I love the game. The training staff has done a great job of jumping on the injury and being proactive. I've been here early, in the pool and running. I'm feeling good."
Chiefs coach Andy Reid said Hali, who has nine sacks this season, has a "good chance" of being available Sunday.
The Chiefs led the Chargers, 14-3, in the first half when Houston left the game. The Chargers scored 38 points after that, including the winning touchdown with less than 30 seconds left.
"Justin and I were in the training room, just watching the game," said Hali, who left the game earlier in the first half. "We could tell that we were needed in the game with our experience and how much we're hungry to get to the quarterback and just knowing what to do out there."
Zombo was signed as a free agent in the offseason from the Green Bay Packers. Moses joined the Chiefs at the start of the regular season as a waiver claim from Green Bay.
Houston and Hali failed to record a sack of Peyton Manning two weeks ago, when the Broncos defeated the Chiefs in Denver to hand Kansas City its first loss.
Information from ESPN.com Chiefs reporter Adam Teicher was used in this report.