I've got the tiles shown below that seem to meet the definition of a National Park. They're all mountains with breathtaking appeal. They're all within the boundaries of my city of Cumae. They are contiguous and form a vertical diamond shape. They have no improvements or districts.
However, my poor Naturalist doesn't seem to recognize this as a potential Park. Is it possibly because the tiles are all Impassable (as are all mountain tiles) so the poor guy can't get there? This would imply that it isn't possible to designate a National Park consisting of all Mountains, which sounds like a bug to me. I'm sure a dedicated Naturalist would find a way to explore the space.
Best Answer
The national park is still a built improvement over a tile, after all, so your naturalist needs to be able to walk on one of the 4 tiles of the park-to-be. This seems confirmed in a discussion from Steam Community here, and from a logic point of view it makes sense: you can't build anything on impassable terrain, and one of the park tiles will contain a small tower and the park's staff cabin.