A report on Israel’s Channel One television said national elections now scheduled for November 2006 could be moved to April or May after Likud lawmakers, angered at the withdrawal, thwarted Mr Sharon's bid to name two cabinet ministers.
"He cannot work like this," the television's political reporter Ayala Hasson said.
"If elections are moved up, Sharon will launch a new party called My Only Country," she said.
Israel Radio quoted a top aide to Mr Sharon as saying a Likud split would be a "done deal" unless party leaders reined in the half dozen hardliners known as "the rebels".
Mr Sharon threatened lawmakers "there will be consequences" after the party rebels saw to the defeat of his Parliament motion to name the new ministers.
There had been speculation Mr Sharon could form a new centrist party to capitalise on broad public support for the pullout that ended 38 years of military rule in Gaza.
But the television report was the first to suggest the process was already underway.
Mr Sharon's political future could at least be partly decided by a leadership election in the left-of-centre Labour Party on Wednesday.
If the incumbent, Vice Premier Shimon Peres, did win Mr Sharon could stay through the end of his term.
Mr Peres's leading opponent Amir Peretz, head of the Histadrut Trade Unions Federation, said he would immediately withdraw from the grand coalition with Likud if elected.
This would force an early national poll.
Opinion polls predicted a Peres victory.
A Channel One survey showed Peres winning 58 per cent to 29 per cent for Peretz, with remaining votes to a third candidate, former party leader Benjamin Ben-Eliezer.