None of the parties involved would comment when reached by The Dispatch, but the paper reported the school has a tentative news conference scheduled for Monday to announce the hiring.
Vrabel, an Ohio State alum, played the past two seasons with the Chiefs after eight years with the New England Patriots. He has been part of NFL's labor negotiations as a member of the NFL Players Association's executive committee.
Luke Fickell, the Buckeyes' former defensive coordinator and linebackers coach, was promoted to head coach on May 30 after Jim Tressel resigned. According to The Dispatch, Fickell and Vrabel were roommates during their time together at Ohio State.
At Ohio State, the 35-year-old Vrabel was a two-time Big Ten Defensive Player of the Year Award recipient before being drafted in the third round of the 1997 draft by the Pittsburgh Steelers.
He signed with New England before the 2001 season and won three Super Bowls as a member of the Patriots.
He was acquired by the Chiefs with Matt Cassel for a second-round pick from New England on the first day former Patriots' executive Scott Pioli could make a move as general manager of the Chiefs in 2009.
In 206 career NFL games, Vrabel has 742 tackles and 57 sacks.
Information from ESPN.com's Bill Williamson contributed to this report.