Knowing very little about this, but wouldn't the National Archives have such a thing?
My own ggg grandfather Fielding Price was held and died in the Yankee Prison in Little Rock and there is a book about that. It's source was the National Archives,
Just found out that my ggg uncle, Frederick Guthrie, 10th Arkansas, Co. D., who was a brother-in-law to Price died there at Camp Morton. The records which shared that information came from the National Archives.
In Arkansas, some nice folks got hold of those Arkansas related National Archives records and put them on the web site relating to the Civil War. I am sorry to say that I do not know if anyone did something like that for Tennessee.
Wherever you live, the state capitol should have some sort of history commission and that should have a copy of them also if you want to visit your nearest place to search.
If someone has written a book about Camp Morton and the men sent there, I would like to know it.
Good luck in your search.