BEREA, Ohio -- The Cleveland Browns are closing in on a deal to add Jameis Winston and make him their backup quarterback behind Deshaun Watson, a source told ESPN.

Winston would replace Joe Flacco as the No. 2 quarterback. Flacco signed with Cleveland midway through last season after a season-ending shoulder injury to Watson. The former Super Bowl MVP went on to lead the Browns in four straight wins as they clinched their first playoff berth since 2020. Flacco led the NFL with 323 passing yards per game over his five starts with the Browns. But Cleveland fell in the first round of the postseason in Houston 45-14.

Winston has spent the past four seasons as a backup quarterback in New Orleans, including 10 starts. Before that, the No. 1 pick in the 2015 draft, out of Florida State, started five seasons for the Tampa Bay Buccaneers. In his final season in Tampa, he threw 33 touchdowns with 30 interceptions.

The Browns also have Dorian Thompson-Robinson on the roster. Thompson-Robinson started three games last season as a rookie.

Also on Tuesday, the Browns agreed to a one-year deal worth up to $3.5 million with running back Nyheim Hines, sources told ESPN's Adam Schefter. Hines, who missed the 2023 season after tearing his ACL in a personal watercraft accident, was released by the Buffalo Bills last week.

Winston has been with the Saints since the 2020 season, most recently as a backup to Derek Carr. He is technically still under contract with the Saints due to a restructure he agreed to in January for salary cap purposes but will be released as a formality.

Winston's last full season as a starting quarterback was in 2019 with the Buccaneers. He led the league in attempts (626), yards (5,109) and interceptions (33) that season, finishing with 33 touchdowns as well. The Buccaneers signed Tom Brady the next offseason, and Winston signed with the Saints as a backup to Drew Brees.

Although Winston won the starting role over Taysom Hill after Brees' retirement, his 2021 season was cut short when he tore his ACL seven games into the season.

The Saints re-signed Winston as a starter in 2022 after attempting to acquire Watson in the offseason. Winston played only three games due to back and foot injuries and was sat in Week 4 to rest his injuries, but he never regained his starting role from Andy Dalton.

Winston returned to the Saints at a reduced salary last offseason to back up Carr. He ended the 2023 season with a controversial handoff to Saints running back Jamaal Williams, who scored after Saints coach Dennis Allen told the team to kneel in a blowout win over the Atlanta Falcons.

ESPN's Katherine Terrell contributed to this report.