Scientists studying the site in northern Jordan found at least 11 sets of human remains buried alongside those of a red fox, along with other animals.
In one grave, a person was buried with the right upper foreleg of a fox, along with a decorated fox skull, according to the researchers from the University of Toronto in Ontario and Cambridge University in England. Another grave contained the complete skeleton of a fox, missing its skull and right foreleg.
It is possible to domesticate the red fox. Still, because of the animal's timid nature, it is a much more difficult task than domesticating a dog. This may explain why dogs wound up as man's best friend.
Other objects found in the graves include stone tools, a spoon made out of bone and the remains of animals including deer, gazelle and cattle.
Previous excavations from a few thousand years later have shown human bodies buried with those of dogs, scientists say.
The researchers stressed that the theory that these animals were pets is just one possibility that happens to fit modern ideas about animals.
"We should remember that some more recent hunter-gatherers consider themselves to have social relationships with a wide range of wild animals, including ones they hunt," said Ted Banning, professor of anthropology at the University of Toronto.
The findings were published in the journal PLoS ONE .