Thompson-Robinson led the Browns on a game-winning field goal drive Sunday as Cleveland defeated the Pittsburgh Steelers 13-10. Thompson-Robinson completed all four of his passes on the final drive. He finished 24-of-43 for 165 yards with an interception.
The Browns worked out Flacco last week following the season-ending shoulder injury to quarterback Deshaun Watson, who is expected to undergo surgery in the coming days.
Flacco has thrown for 42,320 yards and 232 touchdowns in his career. He won the Super Bowl in 2013 while with the Baltimore Ravens and was named Super Bowl MVP.
Flacco, 38, most recently started games for the New York Jets during the 2022 season and led the team to an improbable fourth-quarter comeback in Week 2 in Cleveland that year. In that game, Flacco threw four touchdown passes, including the game winner to Garrett Wilson with 22 seconds remaining.
PJ Walker, who has two starts this year, is the other quarterback on the Browns' roster.
"Joe's role is to support this team," Stefanski said. "He'll be great for that [quarterback] room. He'll be great for this team."
Cleveland is 7-3 and faces the Denver Broncos on the road next weekend.
The Browns lost another key player to injury Sunday. Stefanski confirmed that safety Rodney McLeod Jr. is out for the season with a biceps injury that will require surgery. He replaced starting safety Juan Thornhill on Sunday. Thornhill is battling a calf injury.