Agent Alan Herman confirmed multiple media reports that the Lions have made an offer for Grant, who has played the past five seasons for the Green Bay Packers.
The 29-year-old Grant has played in 63 career games, gaining 4,016 yards and scoring 25 touchdowns rushing. He had back-to-back 1,200-yard seasons in 2008 and 2009.
Grant missed nearly all of the 2010 season after injuring his ankle in the Packers' season-opening game against Philadelphia. He split time with James Starks for the Packers last season.