I have always wondered this myself, so I asked Bogie's vet when Bogie was alive. He said that they do! They may see dream images, because the bird not only lives on instinct, but has a memory capacity as well. Bogie talked up a storm when he slept (at night only) . Sometimes he said human words.
The thing is---What do they dream? I think Ricochet dreams that he is an Eagle who flies high in the sky and has a bunch of girlfriends.