The report on Channel One television on Tuesday said national elections, now scheduled for November 2006, could be moved up to April or May after Likud lawmakers still angry at the withdrawal thwarted Sharon's bid on Monday 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."
Israel Radio quoted a top aide to Sharon as saying a Likud split would be a "done deal" unless party leaders could rein in the half dozen hardliners known as "the rebels".
Sharon had threatened lawmakers "there will be consequences" after the party rebels saw to the defeat of his parliament motion to name the new ministers.
There has been speculation 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 Tuesday's report was the first to suggest the process was already under way.
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, wins Sharon may stay through the end of his term.
Peres' leading opponent, Amir Peretz, head of the Histadrut Trade Unions Federation, has said he would withdraw immediately from the grand coalition with Likud if was elected, and force an early national poll.