ESPN's Adam Schefter reported the news.
Day, 38, was the Buckeyes' co-offensive coordinator for the 2017 season. He spent the previous two seasons serving as Chip Kelly's quarterbacks coach with the Philadelphia Eagles (2015) and the San Francisco 49ers (2016).
Vrabel, 42, was named the Titans' next head coach Saturday. He'll replace Mike Mularkey, who was fired after leading the team to a 9-7 record and wild-card round win over the Kansas City Chiefs this season. The Titans fired him two days after they lost to the New England Patriots in the divisional round.
"Mike has a commanding presence and a deep knowledge for how he will attack this head coaching opportunity," Titans controlling owner Amy Adams Strunk said in a statement. "Throughout his football career, he has played for, been mentored by and coached with successful teams and organizations. He knows what it takes to reach that level of sustained success—he has seen it first-hand. We have a chance to build on the solid foundation that we established over the past couple of years and I believe Mike is the right person to continue that progress.”
Vrabel spent the last four seasons with the Houston Texans, first serving as their linebackers coach before taking over as defensive coordinator in 2017.
Day and Vrabel have a connection through Ohio State, where the latter began his coaching career and played during college. Vrabel served on Urban Meyer's coaching staff as a linebackers coach and defensive line coach before joining Bill O'Brien in Houston.
Being a protege of Kelly is also likely a major factor in his candidacy. Titans quarterback Marcus Mariota thrived under Kelly at Oregon and in a similar system under Kelly's replacement Mark Helfrich. Mariota took a major step back in his development in 2017, throwing for a career low in touchdowns (13) and career high in interceptions (15).
A failure to develop Mariota is seen as a major reason Mularkey was let go.