Al-Khudairi ran in last month's Palestinian elections as an independent with Hamas backing, a spokesman for the group said on Wednesday.
Hamas, which scored a shock victory in the elections, has yet to formally put his name forward to Mahmoud Abbas, the Palestinian president.
If al-Khudairi is not accepted in negotiations with Abbas, or if he turns down the nomination, the group will name Mazen Sonnoqrot, another Hamas-sympathetic independent who is currently Palestinian trade and economics minister.
Al-Khudairi has never addressed key issues such as violence or the recognition of Israel, sticking mostly in campaign speeches to education and job training. He has talked about the need for internal Palestinian reform.
He owns the biggest mattress factory in the West Bank and Gaza, and holds an engineering degree from an Egyptian university.
Abbas has said that he will ask Hamas, whose members won the largest number of seats in the Palestinian parliament in last month's election, to form the new government.
He has called for the new parliament to convene on 16 February.
Exiled Hamas leaders from Syria joined Hamas leaders from Gaza at the Cairo meetings to hammer out the movement's plans for a new Palestinian government after last month's landslide election win.
President Mahmoud Abbas is
yet to approve the selection
Hamas has proposed a national coalition government that will include Fatah - Abbas's party - plus other Palestinian factions and independent figures.
During its meeting, Hamas decided that if efforts to name a cabinet with a non-Hamas prime minister failed, it would name one of its own leaders as the new prime minister, the official said.
"Then Ismail Haniya will be our choice," the official said.
In a news conference from Cairo, Khalid Mishaal, the head of Hamas' political bureau, said Hamas would commit to the Palestinian people.
"We will return consideration to our people in the diaspora," he said.
"We will practise a policy we want and not a policy as the US wants. We will respect the agreements, but refuse in the process to compromise Palestinian interests."
He said he had received good news from Arab and Muslim countries, adding that the Egyptian leadership had not put conditions on Hamas or interfered in the formation of a government.
"Hamas is set to form a national coalition government that could contain all and give opportunities to all qualified Palestinians," he said.
"Hamas does not recognise Israel; no one has the right to force us to recognise it. The political programme of Hamas is resistance till getting back our occupied lands."