Haslam is reportedly desperate to turn around the franchise, which has just one win since the start of the 2016 season.
It's been assumed the retired future Hall of Fame quarterback will seek a top-level front-office role for his next career step. The Tennessee Titans and Indianapolis Colts have been floated as other possible destinations.
Changes in the Browns' decision-making structure might not end there.
Head coach Hue Jackson is believed to be seeking more of a say in personnel choices, reports Ian Rapoport of NFL Network, though there are still questions about his future following Cleveland's 0-9 start to the campaign.