Salah Bardawil, a Hamas spokesman, said that of the 12 cabinet ministers proposed by Hamas, seven are from the West Bank and five from Gaza.
None of the Gaza candidates served previously in parliament or the government, he said.
Azzam al-Ahmed, an aid to the Palestinian president, said after a late-night meeting with Haniya on Friday that the Fatah list could be ready by Sunday and that the government could be formed by the end of the week.
"The Palestinian people are in desperate need of leaders to solve their daily problems and security"
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Abbas and Haniya was originally due to meet on Saturday but it was put back to Sunday.
Under the power-sharing agreement, Hamas can nominate 12 cabinet ministers, including three independents, while Fatah can propose eight, including two independents. Haniya will remain prime minister, while Fatah will be able to fill the post of deputy prime minister.
Salam Fayyad, a former finance minister, is expected to return to the post and is also a leading candidate for deputy prime minister.
The unity deal reached in Mecca did not meet conditions set by a quartet of international mediators for a resumption of aid that was suspended when Hamas came to power a year ago.
The agreement says past Israeli-Palestinian pacts will be "respected", but does not commit the new government to recognise Israel and renounce violence as demanded by the quartet.