On certain days when the sky is clear and the temperatures are extremely cold and there are numerous ice crystals in the air, a rainbow will form in a circle around the sun. These are called "sun dogs" up here in the northland and usually you can only see the sides of the circle (like two parentheses around the sun). They are the brightest rainbows I've ever seen. In answer to your question, clear blue sky is all you will find over these types of rainbows.

Mike