The NFL is expected to begin gathering information to open its investigation into the complaint.
The accusation was made after Texans employee Jack Easterby - who previously worked for New England - attended the Patriots' Super Bowl ring unveiling party June 6, where Caserio was also present.
Houston fired GM Brian Gaine one day after the unveiling party. The Texans haven't been granted permission to interview Caserio to this point, sources told Schefter.
However, the two teams could reportedly potentially come to a mutually beneficial agreement. The Texans could land Caserio as their new GM by sending compensation to the Patriots, whether in the form of draft picks or something else, a source told Mike Florio of Pro Football Talk.
Caserio has been the Patriots' director of player personnel since 2008. He operates as New England's de facto GM and is the top front-office aid to Bill Belichick in player personnel matters.
The Texans also tried to interview Caserio last year before hiring Gaine, but the Patriots denied their request.