Was the Balrog drawn by the ring?

[Leaf]

Originally Posted by Zigûr

It seems to me that if the Balrog was being drawn by the Ring that doesn't mean it knew it was being drawn by the Ring, it may have simply been compelled to follow this urging.

Sure, it may well have been a decision based on curiosity rather than the clear intention to get a hold on the ring of power to archieve some kind of goal.
As a side note: I wonder how exactly the Balrog perceived Frodo. Did the Balrog perceive Frodo as the little, round and ordinary Hobbit, that he is (in a strictly physical way) or was there more to it?! The Orcs at Cirith Ungol mistook Sam for a fearsome and mighty warrior because he had the Ring. I can't remember if Sam was actually wearing the Ring on his finger at this point or not. Furthermore we have Gandalf's notion that Frodo's "appearrance" (or Aura?) wasn't the same anymore (depended on the observer) after he got stabbed by the Morgul Blade.