The players filled roster spots opened by the two-game suspension of defensive back P.J. Williams and the release of linebacker Stephone Anthony.
Zenner, a free agent, is a fifth-year pro out of South Dakota State who spent the previous four seasons with Detroit. He's played in 36 NFL games, rushing 174 times for 685 yards and eight touchdowns. He also has caught 27 passes for 263 yards.
Zenner joins a squad that could be thin at running back this week if Alvin Kamara, who missed practice on Wednesday because of knee and ankle injuries, is unable to play on Sunday.
Parker played in 13 games last season with Denver, catching five passes for 33 yards. He also played on special teams.
Saints tight end Jared Cook has missed Wednesday's practice with an ankle injury.
Williams, who was arrested last offseason for driving while intoxicated, was suspended on Tuesday for a violation of the NFL's substance abuse policy.