The Bengals also came to terms with ex-Cowboy corner Terence Newman this morning, so money could also factor into this decision.
Rivers has been underwhelming after being drafted in the first round out of USC in 2008. Rivers was supposed to come in and be a force as an inside linebacker, but that hasn't materialized.
However, he has been somewhat productive and could be very useful to a team like the Giants who could make his life easier with such a great front four to play behind.
The 25-year-old did miss all of last season with a serious wrist injury.
His best season came in 2010, when Rivers amassed 77 tackles in 15 games after making 72 tackles the year before, albeit in just 13 contests.
New York wouldn't have to give up much, most likely just a mid-to-late-round draft pick.