The team had made an offer to Smith early Friday morning.
The 38-year-old new coach has spent the last decade just up the road with the Tennessee Titans organization, most recently as AFC team's offensive coordinator.
Other reports indicated that Smith had been scheduled to interview with the Detroit Lions this weekend, and was also being eyed by the Philadelphia Eagles.
NFL Network national insider Ian Rapaport said Friday morning that Smith's trip to Detroit was off.
Under Smith, the Titans' offense finished the 2020 regular season ranked number 3 in the NFL in total yards per game and number 2 in rushing yards per game under his leadership.
Before becoming offensive coordinator, Smith served as the team's tight ends coach, assistant tight ends coach, offensive line/tight ends assistant, offensive assistant/quality control coach and defensive assistant/quality control coach.