Green-Ellis, known as the law firm, is one of many backs in New England used in a heavy rotation. While the Patriots would likely want to keep him around, Green-Ellis is probably looking for team that would like to make him their feature back. The Bengals could be that team.
Green-Ellis is a tough, smart runner and while he's not elite, he holds on to the ball and he can get yards when it matters. He may not be a significant upgrade over Cedric Benson, especially if the Bengals don't improve the interior of their offensive line, but, if he has a better attitude, he could definitely be an improvement. The Bengals are expected to select a running back in the draft in the first couple rounds and even if they sign Green-Ellis, or another veteran running back like Michael Bush, they may still do so and go with a similar style of running game that New England has (minus Danny Woodhead).