Not really an eye of course, but it kind of looks like one. This is a close up view of the northern polar vortex on Saturn taken from the Cassini spacecraft. I enlarged the image and enhanced it a little to bring out the details a little more. You can see the original here.
That “eye” is 2,000 km / 1,240 miles across, you can see clouds as them move some 150 meters per sec / 330 miles per hour.
Cassini was 2.2 million km / 1.4 million miles from Saturn at the time the image was taken.