The Italian top-flight has been suspended since March but the league wants the campaign to resume on the weekend of June 13-14 after group training restarted in mid-May.
The announcement comes on the eve of a meeting between Serie A and the Italian government which will determine the fate of the season.
“Pending further investigation, the team as a precaution will resume training individually and at different times tomorrow without the use of indoor areas,” a Bologna said in a statement.
“If the positive case is confirmed, the first team and staff will be put in quarantine,” it added.
On Thursday, Sports Minister Vincenzo Spadafora will advise representatives from the country’s football federation and league if the health conditions are right to return to action.