The clergyman in the Holy See has spent years in the guesthouse known as Santa Maria, where the 83-year-old pontiff has lived since his election in 2013, according to Italian news outlets.
The Il Messaggero newspaper said the sickened man works in the Vatican’s Secretariat of State and a Vatican source said he is believed to be a priest.
The residence has about 130 rooms and suites but many are unoccupied, a source told Reuters.
Francis, who came down with a cold late last month, has canceled public appearances and has been conducting general audiences on TV and online.
On Tuesday, the Vatican said four people have tested positive inside the city-state, but those it listed do not live in the guesthouse.
Santa Marta, which opened in 1996, houses cardinals who come to Rome and lock themselves up in a conclave to elect a new pope.
Vatican spokesman Matteo Bruni told Agence France-Presse he could neither confirm nor deny the latest reports.
Italy has seen more deaths from COVID-19 than any other country, with the latest figures on Wednesday showing that 7,503 people have died in barely a month.