Serie A was suspended indefinitely in March, after some matches were played behind closed doors, due to the coronavirus pandemic, which has claimed more than 145,500 lives globally.
The Italian Football Federation (FIGC) has already stated that the campaign will not resume until the health and safety of all concerned can be guaranteed.
The Italian government has extended its current strict restrictions on movement and outdoor activities until May 3, although reports suggest some clubs are keen to return to training at that time, resume playing by the end of the same month and conclude 2019-20 in July.
Italy – which remains on lockdown – has recorded over 22,100 deaths and at least 168,900 confirmed Covid-19 cases.
On a possibility of resuming training next month, Spadafora told reporters: "The next few weeks will be fundamental to understand the evolution of the healthcare situation and how, if and when we can get back to playing sport at all levels.
"We hope to confirm the May 4 date for a return to training as soon as possible. I hope we can keep to that date, even if it is only for training behind closed doors.
"At this moment, our only concern must be the health and safety of the general population."
FIGC president Gabriele Gravina recently stressed that the 2019-20 Serie A season must be completed despite the coronavirus pandemic.
"I'll repeat what I've been saying: we'll start again once there's the guarantee of everything being in order in regards to the health of the athletes and those who work at the clubs," Gravina told Sky Calcio Club.
"We have a meeting on the 15th of this month between the various technical and scientific bodies to discuss the next steps. We need everyone to be on the same page.
"The hope is we begin again as soon as possible. But we must complete the season - there could be very negative implications if we're unable to do so."