Caserio is reportedly the Texans' top choice to replace Brian Gaine, who was fired Friday after one season at the helm.
Houston was interested in Caserio the last time it needed a general manager, but the Patriots denied the club's request for an interview.
Caserio operates as the de facto general manager in New England's front office, serving as the top aide to Bill Belichick in player personnel matters. The 43-year-old has been with the Patriots since 2001, beginning as a personnel assistant. He's been the director of player personnel since 2008.
Houston head coach Bill O'Brien worked with Caserio from 2007-11 when he was an assistant coach with the Patriots.
Meanwhile, the Texans have already contacted San Francisco 49ers vice president of player personnel Martin Mayhew and former Cleveland Browns general manager Ray Farmer about the vacant GM position.