Just two days out from the scheduled go-ahead for group training at clubs, Parma said all members of their squad and staff had been tested through swabs and blood samples.
All came back negative except for two players, who are asymptomatic.
"Both of them were positive on the first test and negative on the second that was performed 24 hours later," said Parma in a statement on Saturday.
"The players, both in excellent condition and asymptomatic, have nonetheless been immediately isolated and the club will monitor them constantly."
Clubs have suggested June 13 as a date for the championship to restart while group training will get underway on Monday.
However, there is a point of dispute with government insistence on quarantine for the entire team and staff, in the event of a positive test.
Italian clubs favour the German model, where only the infected person is quarantined. AFP SSCSSC