Senior figures in 5-Star, led by former prime minister Giuseppe Conte, were meeting on Wednesday to decide whether to remain in the coalition, having issued a series of policy demands ahead of a vote of confidence on Thursday.
Italy is due to hold a national election in the first half of 2023 and tensions are rising among members of the coalition that Draghi has led for the past 18 months.
Speaking at a news conference in Rome, Matteo Salvini, head of the right-wing League, said his party would not continue to back Draghi if 5-Star withdrew from the coalition.
Early elections were the best solution, he said. "If a coalition party doesn't back a government decree that's it, enough is enough, it seems clear that we should go to elections," he said.
The centre-left Democratic party (PD) is also unwilling to form a new government without 5-Star, a party source told Reuters.
Looking to ease tensions, Draghi said on Tuesday that many of the policy priorities of 5-Star overlapped with those of the government, but warned against continuous demands from coalition partners.
"A government does not work with ultimatums, it loses the point of its existence," Draghi told a news conference, adding he will not be willing to carry on as prime minister if 5-Star pulls out.
The earliest Italy could vote would be in the autumn but it would be unusual to hold an election then as it would overlap with the drawing up and parliamentary approval of the budget law for the next year.
