Saeb Erekat, in a conference said that the timing of the request will be decided next week by the Arab League.
The Palestinians seek a state in the West Bank, Gaza and east Jerusalem, territories Israel captured in 1967.
UN recognition is largely symbolic, since Israel continues to control these territories to varying degrees.
A yes from the world body would endorse the pre-1967 lines as the border of a future Palestinian state. Palestinians fear that border is being erased by Israeli settlement building.
The General Assembly can recognize Palestine only as an observer. A bid to win full UN membership was derailed by insufficient Security Council support in 2011.