In a sense, that’s similar to what we do. Although our minds are capable of thinking much more abstractly and creativity than a rat, our dreams are often just rehashes of memories, often focusing on a very recent experience, thought, or feeling. If a rat, a creature notably less intelligent than a dog, can dream, then it's fair to assume a dog can.
“Humans dream about the same things they’re interested in by day," Dr Deirdre Barrett from the Clinical and Evolutionary Psychologist at Harvard Medical School recently told People Magazine. "There’s no reason to think animals are any different. Since dogs are generally extremely attached to their human owners, it’s likely your dog is dreaming of your face, your smell and of pleasing or annoying you.”
Since their owners are a central part of dogs' everyday experience (and the main trigger of their body's reward system), then chances are they are a central part their dream experience, too.
Exhibit B. Turn up your sound.
Perhaps the hardest question to answer is: Why do dogs dream?
Truth be told, scientists aren’t even too sure why humans dream, so pointing towards some kind of evolutionary advantage for doggie dreams is even harder. A study featured in Nature in 2000 said that the most likely answer was that sleep helps our with memory consolidation and memory reprocessing. It’s likely for dogs, or any mammal, dreaming plays a similar role in helping us condense or realize our everyday thoughts or experiences.