Rivers played all 20 of his snaps on special teams in Thursday's 12-6 win over the 49ers.
Rivers did not record a snap on offense and played 11 snaps on special teams during Sunday's 24-19 loss to the Packers.
Rivers rushed six times for 26 yards during Sunday's 24-18 loss against Chicago.
Rivers rushed twice for nine yards during Sunday's 27-24 victory against San Francisco.
Rivers caught his only target for no gain and played three snaps on offense during Sunday's 41-10 loss to the Cardinals.
Rivers rushed twice for 16 yards during Sunday's 26-20 overtime loss to the Lions.
Rivers "seemingly has the best chance to be the No. 3 running back" for the Rams, according to Cameron DaSilva of Rams Wire.
Rivers signed his contract tender with the Rams on Monday.
The Rams have extended a contract tender to Rivers, Stu Jackson of the team's official site reports.
Rivers rushed 13 times for 52 yards and was not targeted as a receiver in Sunday's 21-20 win over the 49ers.