No details yet have emerged.
Franklin-Myers was in the final year of his deal, making $920,000.
Franklin-Myers, 25, has 15 tackles, three sacks and five quarterback hits in four games.
He entered the league as a fourth-round choice of the Rams in 2018, and he played his rookie season with them. The Jets claimed Franklin-Myers off waivers from the Rams before the 2019 season.
Franklin-Myers did not play in 2019, spending most of the season on injured reserve, but he had 19 tackles and three sacks in 15 games last season.
UPDATE 9:36 PM ET: Bien-Aime updates it’s a four-year, $55 million extension with $30 million guaranteed.