The epidemiological role of domestic animals in the spread and transmission of SARS-CoV-2 to humans has been investigated in recent reports, but some aspects need to be further clarified. To date, only in rare cases have dogs and cats living with COVID-19 patients been found to harbour SARS-CoV-2, with no evidence of pet-to-human transmission. The aim of the present study was to verify whether dogs and cats act as passive mechanical carriers of SARS-CoV-2 when they live in close contact with COVID-19 patients. Cutaneous and interdigital swabs collected from 48 dogs and 15 cats owned by COVID-19 patients were tested for SARS-CoV-2 by qRT-PCR. The time elapsed between owner swab positivity and sample collection from pets ranged from 1 to 72 days, with a median time of 23 days for dogs and 39 days for cats. All samples tested negative, suggesting that pets do not passively carry SARS-CoV-2 on their hair and pads, and thus they likely do not play an important role in the virus transmission to humans. This data may contribute to confirming that the direct contact with the hair and pads of pets does not represent a route for the transmission of SARS-CoV-2.