Stoops apparently interviewed for the job Wednesday but was back on the road recruiting for the Wildcats that night. Although he as ties to Rice athletic director Chris Del Conte from Del Conte's days as an associate athletic director, it was not enough for him to remain in the hunt for the job vacated by Todd Graham. Graham left for the head coaching job at Tulsa.
Stoops also has ties to the Houston area as a former assistant with the Houston Cougars.
Former Miami head coach Larry Coker also withdrew his name from consideration.
Stoops is slated to return for his fourth year as Arizona's defensive coordinator.