Both candidates are reportedly already beginning to assemble staffs in case they land the role.
The head coaching hire will be extremely important for Houston as quarterback Deshaun Watson's future remains uncertain. Schefter previously reported Watson was "furious" about the process of hiring general manager Nick Caserio.
It's unknown if any coach would be able to convince Watson to stay, but the quarterback has spoken to Patrick Mahomes about Bieniemy in the past.
Bieniemy has been arguably the most successful offensive coordinator in the NFL over the past three years with the Kansas City Chiefs. The team has led the league in total yards from scrimmage twice in those three seasons, including in 2020, while the 2019 squad went on to win the Super Bowl.
Kansas City hosts the Buffalo Bills on Sunday with a trip to the Super Bowl on the line.
That game could be a test for Frazier, who is in his fourth season as the Bills defensive coordinator. The 61-year-old led a unit that ranked second in points allowed and third in yards allowed in 2019, while the defense has remained solid in 2020 on the way to a 13-3 season.
Buffalo especially thrived defensively in last week's 17-3 AFC Divisional Round win over the Baltimore Ravens.
Frazier also has previous head coaching experience, producing a 21-32-1 record across four seasons with the Minnesota Vikings.
One of these two could be the next coach of the Texans, although they will also have to compete with other candidates, including former Lions head coach Jim Caldwell, Colts defensive coordinator Matt Eberflus, Ravens assistant coach David Culley and former quarterback Josh McCown.