Jets TE Chris Herndon is suspended for the first four games, which opens the door for Griffin to step in secure a spot.
During the draft, Griffin was arrested and charged on Friday night after he allegedly became “disorderly” and punched through a window at a Nashville hotel.
Griffin was charged with vandalism over $1,000 and public intoxication and later released.
Griffin, 29, is a former sixth-round pick of the Texans back in 2013. He was in the second year of his three-year, $9 million contract that includes $3.225 million guaranteed and set to make a base salary of $2.25 million for the 2019 season when the Texans released him a few months ago.
In 2018, Griffin appeared in 14 games for the Texans and caught 24 passes for 305 yards receiving and no touchdowns.