Two Serie A clubs, Torino and Fiorentina, separately think that the 2019/2020 season is unlikely to finish due to the coronavirus pandemic.
Italy has been the hardest-hit country in the world with more than a third of all global fatalities coming from the European nation. The country has reported 11,591 deaths from Covid-19.
The country is currently under lockdown for the last three weeks and all sporting activities were halted with no return date announced.
"Let's think about health now, we'll talk about football later," Fiorentina owner Rocco Commisso told state broadcaster RAI in a radio interview.
"We'll see if we can get back to training. But there's a serious possibility that the championship won't end."
His Torino counterpart Urbano Cairo said that, even if teams could start training again in May, there would not be time to complete the championship.
"That would mean starting training at the end of May and then starting the games at the end of June, playing in July and August," he told another RAI radio channel.
"Then give everyone a month off, a month to train and you would not start the next championship before November. It can't be done."
Cairo spoke against awarding the title to leaders Juventus saying that the league is not yet over.
"It should not be assigned because the championship isn't over and there are three teams in the running," he said.
Juventus top the standings on 63 points, one ahead of Lazio and nine in front of Inter Milan who have a game in hand.