The novel coronavirus SARS-CoV-2 likely emerged from a wildlife source with transmission to humans followed by rapid geographic spread throughout the globe and dramatic impacts on both human health and global economies. Since the onset of the pandemic, there have been several instances of human-to-animal transmission involving companion, farmed and zoo animals, and one instance of infection in a wild mink, with the clear potential for further spread into free-living wildlife. The establishment of reservoirs of infection in wild animals would create significant challenges to infection control in humans and could pose a threat to the welfare and conservation status of wildlife. Herein, we discuss the potential for exposure, maintenance and onward transmission of SARS-CoV-2 in an initial selection of wild and feral species (bats, canids, felids, mustelids, great apes). Targeted surveillance and dynamic risk assessment are important tools for the early detection of infection in wildlife and a means of collating and synthesising emerging information in a rapidly changing situation. Such efforts should be integrated with public health information to provide insights into the potential role of wild mammals in the continuing epidemiology of SARS-CoV-2. This approach should also be adopted to address the wider need to proactively assess threats to human and animal health from other diseases that may emerge from wildlife.