The free agent has "an offer on the table from the Patriots," according to CSN New England. Blount, 30, had 18 touchdowns and 1,161 yards on 299 carries last season for the Super Bowl champions.
The deal is expected to be for less than $2.5 million annually, but have incentives, according to the report.
New England has been busy in free agency this offseason, even at the running back position. The franchise signed Rex Burkhead in March and hosted Adrian Peterson for a visit on Monday. It also currently has Dion Lewis, James White, D.J. Foster, Brandon Bolden, and James Develin on its roster.
Pro Football Talk speculated that this is "Blount's last best chance for a lucrative NFL contract."
NFL.com reported last week that there is mutual interested in a reunion between Blount and the Patriots. The running back was also a free agent last season, before signing a one-year, $1 million pact.