Peter Jackson I suspect. Was there some Tolkien artwork that featured a big eye, though?
I Googled it, and somebody on the internet says this:
"Peter Jackson decided to throw in a line about how Sauron could not yet take physical form, hence the flaming eyeball. This wasn’t in the book. I think Jackson didn’t want to show an embodied Sauron, which would have made him seem less threatening and like just another movie monster.
In the book, we have only the vaguest of hints about what Sauron looked like. He was larger than a man, and man-like, but not gigantic. Gollum saw him in person and said that he was missing one finger. His skin was black. When he was killed at the end of the Second Age, it was also hot enough to set someone on fire, and it probably retained that quality when he reincarnated himself in the Third Age.
I believe, and others may reasonably disagree, that the Eye of Sauron was actually an image that appeared in the minds of people who were sensitive to it. Galadriel could see it. Frodo saw it at times, and could feel it looking for him. As he got closer and closer to the Cracks of Doom, it got to the point where he could see nothing else. It filled all his mind.
Filmmakers are obliged to make the abstract concrete, and the ambiguous specific. Jackson decided to create the eyeball as a practical representation of the Eye of Sauron. It worked pretty well."