Per NFL Network's Ian Rapoport, Mularkey could be fired if the Titans lose to the Chiefs.
Rapoport added the Titans are prepared to take a run at New England Patriots offensive coordinator Josh McDaniels if they don't bring Mularkey back.
Mularkey first took over as the Titans' interim head coach for the final nine games of the 2015 season after Ken Whisenhunt was fired.
The Titans took the interim tag off Mularkey in January 2016. The 56-year-old led them to a 9-7 record last season, their first winning record since 2011, but they failed to make the playoffs after losing a tiebreaker to the Houston Texans.
Tennessee limped to the finish line this season, snapping a three game losing streak with a 15-10 victory in Week 17 against the Jacksonville Jaguars to secure a playoff berth for the first time in nine years.
Mularkey has a 20-21 record as Titans head coach. He previously coached the Jaguars and Buffalo Bills, and has compiled a 36-53 career record in six seasons with three teams.