The 31-year-old spent seven seasons with the Giants after being drafted in 2005, winning two Super Bowls in the 2007 and 2011 seasons.
Tom Coughlin is seeking a veteran presence in his backfield following a spate of turnovers from his backs in his side's defeat in their season opener against the Dallas Cowboys.
He feels that Jacobs fits the bill and has the advantage of being familiar with their system. The former San Francisco 49ers man could be signed in time to the face the Denver Broncos in week two, reports Fox Sports.
The Giants are currently without starting back Andre Brown after he broke his leg in pre-season.