The soon-to-be 29-year-old Addai was a first-round pick of the Colts in 2006, but has been felled by injuries in recent years and has played in just 20 games over the last two seasons. However, he is regarded as a solid pass-catcher out of the backfield and good in pass coverage.
Hightower is not quite 26, though he is rehabbing a torn ACL suffered while playing for the Redskins last October. Grant, 29, was a backup for the Packers last year. Green Bay has told Grant it is interested in bringing him back, but he is exploring his options.
With BenJarvus Green-Ellis now a Bengal, Danny Woodhead is the most veteran member of the Pats' running back group, which also includes last year's draft picks, Shane Vereen and Stevan Ridley.
New England was interested in former Raider Michael Bush before he signed with the Bears, but Bush's price tag was too steep; he got a four-year, $14 million deal from Chicago, with $7 million guaranteed.
ESPN first reported the visits of Hightower and Grant.