The relief, if approved by the league, would allow the Rockets to trade for a player making up to the midlevel exception of $5.7 million, or sign a free agent, according to the report.
On Friday, when Yao's injury was made public, Rockets general manager Daryl Morey said the team would explore the disabled player exception option, among others, to soften the blow of Yao's absence.
In 2009, when the Rockets lost Yao for an entire season with a hairline fracture in his left foot, the team sought and obtained a disabled player exception that allowed it to sign Trevor Ariza as a free agent.
If the NBA approves the request, the Rockets would have 45 days to use the exception, dated from the day the injury was discovered, according to the report.
The injury was diagnosed in an MRI exam Thursday, and the team announced Yao would be lost for the season a day later. Team physician Walter Lowe said surgery is the usual treatment for such an injury, which has sidelined Yao since Nov. 10.
If Yao chooses surgery, it could be up to 10 months before he can return to the court.
The seven-time All-Star sat out last season after reconstructive surgery to repair his broken left foot. Lowe said this injury is related to last year's. He said the reconstructive surgery on his foot does not put Yao at a greater risk of stress fractures, but that he always has been prone to them.
Yao's reconstructive surgery was to make the foot flatter and help distribute the stresses.
Yao is due to make $17.7 million this season after signing a five-year contract extension in September 2005.
The Rockets went 42-40 and missed the playoffs with Yao on the sideline last season, and are just 13-15 this season, next to last in the Southwest Division.
Information from The Associated Press was used in this report.