Cooter and the Lions mutually parted ways at the end of the 2018 regular season, ending his five-year run with the organization.
He joined Detroit's coaching staff as the quarterbacks coach back in 2014. When offensive coordinator Joe Lombardi was fired during the 2015 season, Cooter took over and was in charge of the offense for the past three-plus years.
Detroit's offense ranked 21st in Cooter's first full season as offensive coordinator in 2016 and jumped up to 13th in 2017 before regressing down to 24th this past season. The Matthew Stafford-led Lions averaged 22.5 points per game over the last three seasons.
The 34-year-old Cooter was previously a part of coaching staffs in Indianapolis, Kansas City and Denver as well.
Cleveland has an opening at offensive coordinator after promoting Freddie Kitchens to head coach earlier this week. According to Rapoport, the Browns are interviewing former Tampa Bay Buccaneers offensive coordinator Todd Monken for the job.