Citing a source familiar with the Rams' plans, Rapoport reported Monday that Finnegan would have to take a "sizable" pay cut to remain on the roster.
The corner is set to count $10 million against the Rams' salary cap. The team would save $4 million by cutting him.
Finnegan's play has fallen off precipitously the last year and a half. The Rams feel he looked slow in 2013; one St. Louis source told Rapoport the team saw it in training camp last season.
The 30-year-old appeared in just seven games in 2013 before being shelved for the season in November. He didn't perform well when he was healthy. Pro Football Focus graded Finnegan its 109th rated corner out of 110.
In our offseason forecast, we predicted Finnegan could be a cap casualty unless he was willing to restructure his contract. As Finnegan's play has tanked, Rapoport indicates that the cornerback would have to take a discount if he wants to continue playing under Jeff Fisher. The other option is to face being an aging veteran on the open market.