Hamas has submitted its list of nominees for the new cabinet to the Palestinian Authority president.
Mr Haniya is likely to appoint party loyalists to his cabinet
The group was unable to persuade any rival factions to join a coalition.
Mahmoud Abbas is expected to approve the list, but has warned a failure by Hamas to adopt a more moderate position could hurt Palestinian interests.
Meanwhile, food shortages in Gaza continue as Israel and the Palestinians have failed to resolve a dispute over the closure of a border crossing.
"People will go to bed tonight hungry," the UN's David Shearer told the BBC.
Israel has closed the Karni crossing over security concerns. It has said it will open a smaller crossing but the Palestinians have rejected the offer.
Reports say Hamas is likely to appoint party loyalists to key cabinet positions after failing to engage moderate groups, and in particular, its main rival Mr Abbas' Fatah party.
Early reports suggest the Hamas leader Mahmoud Zahar will be appointed as the new foreign minister by Prime Minister-designate Ismail Haniya.
The BBC's Alan Johnston in Jerusalem says Hamas had wanted to form a broad-based coalition government of national unity.
Having all the major positions occupied by Hamas leaders will be the start of a new and very uncertain era in Palestinian politics, he says.
On Sunday evening, the US summoned Israeli and Palestinian negotiators to an emergency meeting to discuss the closed Karni border crossing - which is causing severe food shortages, the UN says.
The two sides failed to reach an agreement, but have reportedly agreed to more talks on Monday morning.
Up to 1.3 million people in Gaza - half of them children - could be going without bread soon, Mr Shearer of the UN office for humanitarian affairs warned.
Bakeries had begun to close for lack of flour, leaving people without a staple of their diet, he said.
"Unless food stocks come in, we can't see an end to this," he told BBC World television.
Israel and the Palestinians have feuded over the Karni crossing before. Last year, US Secretary of State Condoleezza Rice brokered a deal to keep it open except in case of immediate security threats.
But it has been open for only a few weeks since the beginning of the year.
Bakeries may have to close for lack of flour, the UN says
Critics of Israel say it is imposing collective punishment on the Palestinians of Gaza for bringing Hamas to power.
Israel denies it, saying it faces specific security threats.
"We'd like Karni to be fully functioning as soon as possible. The only reason Karni is closed is the definite terror warnings," foreign ministry spokesman Mark Regev said.
Hamas was the surprise winner of Palestinian elections in January, taking well over half the seats on the Palestinian Legislative Council.
Fatah, previously the dominant force in Palestinian politics, ruled out joining a Hamas-led government on Friday after Hamas refused to uphold previous peace agreements with Israel.
Correspondents say a government without Fatah will make isolation from Israel and the US more likely.
Israel, the EU and the US regard Hamas as a terrorist organisation.
The EU and the US are talking of cutting crucial flows of aid funding if a Hamas-led government refuses to lay down its arms and pursue peace with Israel.