I always imagined the Leviathan to have serpent-like characteristics due to the omnipresent Naga symbol the Leviathans revere. The symbol is constantly referred to during the Leviathan sequence. The Leviathan must also have appendages like feet and possibly hands because it leaves footprints and can open doors. Additionally, the Leviathan monster is so visually horrifying that anyone who sees it will potentially go mad. Therefore, I imagine the Leviathan monster as a disturbingly hideous Lovecraftian being with snake-like characteristics (for example a bunch of snake-heads writhing in its mouth?) who has a somewhat humanoid form.
 At some point, I'm hoping to get an artist friend of mine to draw an interpretation of the Leviathan. I'll post it when/if he ever draws the true fetid form of that "insufferable pig" Jebez Hawkes!
~PennyDreadful~Â