The way I think of it is, anywhere that has nerve endings or a nerve supply, in theory, can take damage as your myelin is eaten away.
Though the liver has no direct inner nerve paths through it, it does have a supply to the bile duct and surrounding areas, portal veins and hepatic arteries. Otherwise the blood supply would not be under control.

So I think that where there is a nerve, there could be damage.
Now whether this damage can cause pain, discomfort or sensations is another matter.
But if nerve damage in the spine can cause you to feel 'water running down a leg' , then I think anything is possible.

Take it easy.