Rivera does not have practice squad eligibility remaining, so the Patriots would have to make a corresponding move on their 53-man roster.
The 26-year-old Rivera originally joined New England as a member of the practice squad in 2011. He earned a spot on the 53-man roster to begin the 2012 season, playing in two games as a reserve linebacker and special-teams player before being released.
Rivera later signed with the Dolphins, playing in one game. He was placed on injured reserve and released with an injury settlement earlier this month.
The possible re-signing of Rivera could be related to the health of linebacker Tracy White, who has been out with a foot injury for the last two games. The Patriots promoted Jeff Tarpinian from the practice squad on Saturday, and he played in Sunday's win over the New York Jets.