Henry, 26, is scheduled to make $10.27 million this season and become a free agent in the offseason.
The Pro Bowler rushed for a league-leading 1,540 yards last season with 16 touchdowns.
He became the first player to have 180 yards or more rushing in three consecutive games, counting the season-finale win over the Houston Texans and playoff wins against the New England Patriots and Baltimore Ravens.
The 6-foot-3, 247-pound Henry added 446 yards with two touchdowns in the playoffs.
ESPN’s Turron Davenport contributed to this report.