The Rams have $99.6M in cap space in 2019, second most in the league behind the Jets ($103M).
Unrestricted free agents after this season as listed on overthecap.com (https://overthecap.com/free-agency) : Joyner, Austin, Saffold, Gurley, Donald, Peters, Cooks, Longacre, Easley, Shields, Westbrooks, Havenstein, Brown, Mannion, Hager. The Rams will undoubtedly pick up Gurley's 5th year option so he won't really be a FA until after the 2019 season. And I'll add Suh to the list. (I guess overthecap is lagging a bit.) Looks like the money is there for the guys the Rams target as core players: if the deal doesn't get done it will be for some other reason. Keep in mind that if someone (Suh?) leaves via FA that could generate a comp pick in the 2020 draft.
The Rams have the most cap space in the league in 2020 ($168.9M), well ahead of 2nd place Buffalo ($158.3M).
Overthecap.com shows these guys as UFAs after the 2020 season: Whitworth, Brockers, Talib, Goff, Sullivan, Zuerlein, Higbee, Cooper, Christian, Hemingway, Allen, Thomas, Blythe, Nixon. The Rams will pick up Goff's 5th year option so he'll get pushed out to 2021. Gurley will be in this FA class, though. Again, it looks like the money is there for the guys the Rams will want to hang on to.
Right now the only current Rams who would be FAs in 2021 are Woods and Goff.
AlbaNY_Ram