Ohio State quarterbacks coach and co-offensive coordinator Ryan Day could be headed back to the NFL, ESPN's Adam Schefter reported.
Kelly was Day's college coach at New Hampshire and also started his coaching career at the school under Kelly.
Vrabel and Day have never worked together, but Day may be under consideration because he worked for Kelly, who was Titans quarterback Marcus Mariota's coach for part of his college career at Oregon.
That connection might be appealing to the Titans because Mariota's pro career has not taken off as fast as expected.
Mariota's lack of development is considered one reason why former head coach Mike Mularkey was not retained despite leading the Titans to the playoffs in 2017.
Day received praise for his work at Ohio State this past season with quarterback J.T. Barrett, who improved his passing accuracy under Day to a 64.7 percent completion rate with 35 touchdowns and nine interceptions.
Under the direction of Day and co-coordinator Kevin Wilson, Ohio State finished seventh in the country in total offense in 2017.
Vrabel played at Ohio State during the 1990s and returned to the school in 2011 as a linebackers coach under Luke Fickell. He stayed on for two more years as defensive line coach after Urban Meyer was hired as head coach before leaving to join the Houston Texans.
Meyer said earlier that Day had turned down offers to be a head coach in the Southeastern Conference to remain at Ohio State.