Perriman, 27, is a five-year NFL wideout who spent the 2018 season in Cleveland before playing for the Bucs in 2019 and the New York Jets in 2020.
The Browns are coming off a successful season, as they went 11-5 and reached the playoffs for the first time since 2002. They also won their first playoff game since 1994 and fell just short of the AFC Championship Game, losing a heartbreaker to the Kansas City Chiefs.
While there is a lot to like about Cleveland's roster entering the 2021 season, there are plenty of holes to fill as well.
Linebacker may be the biggest need on defense in support of a supremely talented front four, and David would likely thrive behind the likes of Myles Garrett and Sheldon Richardson.
David is a one-time Pro Bowler and one-time First Team All-Pro, but it can be argued that he has been snubbed many times throughout his career given his production.
The former Nebraska standout has missed just seven regular-season games during his career, and he has finished with 100 or more tackles in a season eight times.
Last season, David started all 16 games and registered 117 tackles, three forced fumbles, two fumble recoveries, 1.5 sacks and one interception. He also started each of Tampa's four playoff games.
David is one of the top free-agent linebackers and figures to receive a big contract. His durability, productivity and experience would provide a big boost to a Cleveland defense that ranked 17th in total defense and 21st in points allowed last season.
Offensively, the Browns made strides last season, as the running game contributed 2,374 yards thanks largely to Nick Chubb and Kareem Hunt, while quarterback Baker Mayfield bounced back with a solid season.
Mayfield completed 62.8 percent of his passes for 3,563 yards, 26 touchdowns and eight interceptions, and he did it despite being without No. 1 wide receiver Odell Beckham Jr. for nine games.
Jarvis Landry was the leading receiver with 72 catches for 840 yards and three scores, and no other wideout on Cleveland's roster finished with more than 37 receptions or 599 yards.
Rashard Higgins was the Browns No. 2 wide receiver when Beckham was out last season, but he is a free agent and could be on the move despite Cabot noting that the Browns would like to re-sign him.
Perriman has not lived up to his billing as the No. 26 overall pick in the 2015 NFL draft by the Baltimore Ravens, but he has shown signs of life in recent years.
In his one season with the Browns, Perriman built chemistry with Mayfield, finishing with 16 grabs for 340 yards and two touchdowns.
He followed that up with the best season of his career in 2019, racking up 36 catches for 645 yards and six touchdowns in Tampa. He was especially productive late in the season when Mike Evans and Chris Godwin were injured.
Perriman ended up in a tough situation last season as part of a lackluster Jets offense, but he still managed 30 receptions for 505 yards and three scores.
Cabot reported that the Browns want more speed in their receiving corps, and since Perriman is a speedster who averages 16.5 yards per catch during his NFL career, he could be an ideal fit who shouldn't break the bank.