NFL.com's Lance Zierlein said he has spoken to NFL personnel who said they believe Morey could "absolutely do the job" of an NFL general manager if he has "capable evaluators around him."
Morey, who spent 13 years as the Rockets' GM beginning in 2007, stepped down from his position Thursday, according to ESPN's Adrian Wojnarowski.
During his time in Houston, Morey constructed a team that qualified for the playoffs 10 times, including each of the past eight seasons.
The Rockets reached the Western Conference Finals twice during Morey's tenure and came within one win of reaching the NBA Finals in 2018, but they were never quite able to break through.
Morey's biggest move in Houston was the acquisition of guard James Harden from the Oklahoma City Thunder, as Harden went on to become an NBA MVP and perennial All-Star after joining the Rockets.
Also, Morey acquired Russell Westbrook from the Thunder last offseason, but Houston was unable to get past the second round of the playoffs despite the move.
The 48-year-old Morey is known for his heavy use of analytics when it comes to constructing a roster, as he majored in computer science with a focus on statistics at Northwestern before working as a consultant with STATS, Inc.
In his tweet, Zierlein alluded to the possibility of Morey landing with the Houston Texas, as the Texans fired head coach and general manager Bill O'Brien last week.
While Morey has given no public indication that he plans to pursue an NFL job, the Texans would be a logical organization for him to join since he is already so deeply rooted in the Houston area.
Making the transition from a different sport to the NFL in a front office role isn't unheard of, as Paul DePodesta notably held significant positions with MLB's Los Angeles Dodgers, San Diego Padres and New York Mets before joining the Cleveland Browns as their chief strategy officer in 2016.
That move hasn't necessarily led to on-field success for the Browns until this season, as they are off to a 4-1 start, but perhaps that could serve as a template for Morey if he is considering a transition.