The resistance movement is a powerful force in the territory that Israel has held since the 1967 Middle East war, but which Prime Minister Ariel Sharon now aims to quit under a plan to "disengage" from the Palestinians.
Palestinian officials said on Tuesday the offer to Hamas had been made last week. Hamas officials said they were drawing up a response.
"If it is approved, it could form a plan to deal with the situation that may arise in the event of an Israeli withdrawal," said Qais Abd Al-Karim, a senior official of the PLO's Marxist Democratic Front for the Liberation of Palestine (DFLP).
But the proposed decision-making body would only be temporary and not replace the PLO. It would remain under the control of Palestinian President Yasir Arafat, something Hamas officials appear uneasy about.
Arafat's PLO brings in most factions. But past calls to join have been resisted by Hamas and Islamic Jihad members, who have sworn to destroy Israel rather than seek a state alongside it in Gaza and the West Bank.
The popularity of Hamas is boosted by a charity network that has helped fill a vacuum left by the ailing Palestinian Authority.
No aims to seize Gaza
US officials have said they fear a Hamas takeover if Israel withdraws troops and about 7500 settlers who live in Gaza alongside more than 1.3 million Palestinians.
But Hamas has said it does not aim to seize Gaza and last week finalised its own plan for sharing power.
"The unilateral decision-making that dominated in the past has harmed the Palestinian cause. All political groups should share in political decision-making"
"The unilateral decision-making that dominated in the past has harmed the Palestinian cause. All political groups should share in political decision-making," Hamas official Sayyid Siyam said.
Palestinians welcome any pullout from Gaza, though they fear it could be at the expense of a stronger Israeli hold in the West Bank. Sharon is due to seek US support for his Gaza plan in Washington next week.