Griffen, 33, was selected by Minnesota in the fourth round of the 2010 NFL draft and spent a decade with the Vikings.
He signed a one-year deal with the Dallas Cowboys in August 2020 and was traded to the Detroit Lions two months later.
Wonnum have been the front-runners throughout the preseason, but the team left the door open for more competition at that spot when it brought in Griffen for a workout last week.