The bad news is that cats can easily become infected with different forms of the coronavirus. The good news is there is no evidence that suggests your cat will contract COVID-19--or that they can give it to you.
Here's the scoop (no pun intended):
The majority of felines are already infected with a benign version of the virus. Feline enteric coronavirus (FECV) lives in their intestines and usually produces no more symptoms than vomiting or mild diarrhea. Usually, if the virus is present the kitty will recover without veterinary intervention. Per the Merck Veterinary Manual, 40% of all pet cats and 90% of cats in multi-cat households are susceptible.
While FECV is generally a minor nuisance, the virus can mutate into the serious and deadly feline infectious peritonitis (FIP). It is not understood how this happens or why, but it has been determined that multi-cat households are more likely to see FECV and other strains of feline coronavirus mutate into FIP. The instance is higher due to more contact, but still the mutation is rare.
Symptoms of FECV tend to go undiagnosed, but with FIP the vet must piece together symptoms while ruling out other diseases. These concerns tend to be highest among rescue shelters and breeders. When cats are housed in small groups of 3-4, that helps in minimizing contact. Also, they must have adequate litter boxes that are kept clean and regularly disinfected.
In spite of separation and sterile environments, cats can still spread infectious particles to each other. If the virus mutates to FIP, the prognosis is poor. An existing FIP vaccine has proven not very effective, and it is not recommended.
Obviously, the feline version of coronavirus is a sidebar to the spreading of the human version. Still, it is good to be vigilant without spreading fear. Consult only reliable sources like the World Health Organization's Guide to Coronavirus, but don't run out to buy kitty their own surgical masks!