Angel Almendros, of City University in Hong Kong, told BBC News: "There is not a single case of a pet dog or cat infecting a human being with COVID-19".
To avoid any risk of pets carrying the virus from the hands of the owners, the president of the British Veterinary Association (BVA), Daniella Dos Santos, encouraged the owners to take "sensible precautions".
She said: "Practice good hand hygiene, try to keep the cats indoors.
"Avoid unnecessary contact with your pets, hugging or licking your face and don't touch other people's dogs while walking."
Angel Almendros, in a recent article on the subject, cited the case of a 17-year-old pet dog in Hong Kong who tested positive for COVID-19.
Thought to be infected by its owner, the dog was later released from testing after being released from the virus.
Shortly after its release, the dog died tragically, probably as a result of the stress induced by the testing process, the Hong Kong vets said.
Almendros said: "But even where we have these positive results, animals are not getting sick.
More recently, there have been reports that tigers at the Bronx Zoo in New York he had contracted the virus from a worker carrying the virus, but he was asymptomatic.
"It is interesting to note in the experimental evidence that cats can be infected, in addition to the apparent infection of a tiger," said Bryan Charleston, director of the Pirbright Institute in the UK, which specializes in the study of infectious diseases.
All of this led "evidence of transmissibility" to build a solid case.
In addition, there is also evidence that humans can transmit respiratory infections to large wild monkeys.
This makes the global spread of the virus a particular concern for conservationists working to protect endangered wildlife around the world.
In all the cases mentioned, infected humans are the animals that pose the greatest threat to other species.
Professor Charleston said: "We know that the virus jumped from an animal to a human (at the beginning of this crisis), but that seems to be because people were eating these infected animals."
Relating the information to cats, the British Veterinary Association draws attention to how an animal's fur can transmit the virus for a time "if a pet comes into contact with someone who is sick".
So, advice to keep pets indoors for the near future.
Almendros recommended: "Treat pets like other people in your home.
"So, if you're feeling sick, you better not interact with them."