Yahya Moussa, a Hamas member of parliament and senior leader, told Reuters news agency on Sunday: "We have agreed on the political platform of the new government.
"The Hamas movement has also agreed that the next prime minister will not be Haniya."
Hamas took office in March after beating Fatah in parliamentary elections, but has struggled to govern after foreign donors suspended their aid donations and Israel refused to release revenues it collects on the government's behalf.
Palestinians hope the creation of a unity government will allow the blocked funds to flow again.
"The choice has been made for the next prime minister," Moussa said.
"His name will be presented to President Abbas. A joint committee will be formed to appoint the portfolios and to finalise other details."
An earlier deal to form a unity government collapsed several weeks ago. The main stumbling block has been Hamas's refusal to recognise Israel.
Mustafa Barghouthi, an independent MP who has been mediating between Hamas leaders and Abbas, confirmed that a tentative deal had been reached.
"There is approval to form a new government headed by a new prime minister," he said.
"We are preparing for a meeting between President Abbas and Prime Minister Haniya very soon."
But Fawzi Barhoum, a Hamas spokesman, was less upbeat.
He said an agreement was "imminent", but that important details would still have to be worked out. He did not elaborate, but said Hamas would have the right to form the cabinet and the name the prime minister under any deal.