The Browns, though, say that the report is untrue, according to ESPN's Adam Schefter.
Tressel, 61, hasn't coached since 2010 when Ohio State finished 12-1. However, the season was vacated due to Tressel knowingly using ineligible players. He resigned from his position as head coach prior to the 2011 season and faces a five-game suspension if he returns to the collegiate coaching ranks any time before the 2017 season.
Since his resignation, Tressel has served as a consultant for the Indianapolis Colts and a non-athletic position at the University of Akron.
In 10 seasons with the Buckeyes, Tressel compiled a 106-22 record (including the 12-1 season in 2010), and a national championship victory in the 2002 Fiesta Bowl.
The Browns fired coach Rob Chudzinski after his team finished 2013 with a 4-12 record and a seven-game losing streak to end the year.