The heads of Fiorentina and Torino said in separate interviews on Monday that they believed that the Serie A season was unlikely to finish due to the coronavirus pandemic.
Italy, the world's hardest hit country which accounts for more than a third of all global fatalities, saw its total death tally rise to 11,591 on Monday.
Italians have been under lockdown for three weeks and Serie A, like football competitions around the world, is at a standstill with no indication of when it may restart.
"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."
He was against awarding the title. "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.
(Writing by Brian Homewood; Editing by Christian Radnedge)
