This may be a hot take, but I'm not that high on them signing him. I understand how good he is, but the Rams always look at the transactions with 1 or 2 years down the road in consideration. I think they hoped to re-sign VM and OBJ when they obtained them, but I think they were more than prepared to lose them. While losing Woods hurts and I'm less optimistic about OBJ re-signing before he is healed, I expect the Rams to adapt their offense to involve more TE's (Higs, Hopkins/Blanton), Harris, and even Tutu. If Skowronek can learn to catch the ball with consistency, he's not a bad 5th receiver.
Look at the defensive players who are up for FA next year:
Greg Gaines
A'Shawn Robinson
Travin Howard
David Long
Nick Scott
Taylor Rapp
I think re-signing Gaines and Robinson is more important than getting Wagner. If they get him, great. If they don't? They may be in a better situation going forward being able to re-sign Gaines, Robinson, Howard, Long, and Scott.