"The draft that will be presented today is the French draft based on Palestinian observations and decisions," Malki told the AFP news agency."It will be presented to the Security Council as a blueprint and could be put to a vote 24 hours after that."
The vote may be later if no Security Council member asks for the vote to be taken, he added.
Malki met French Foreign Minister Laurent Fabius on Tuesday along with Arab League secretary general Nabil al Arabi to discuss the draft resolution.
It was not clear whether the Palestinians had insisted on a two-year deadline for the removal of Israeli soldiers from Palestinian territories that was in their original draft.
The French agreed to drop a demand that the Palestinians recognise Israel as a Jewish state, Malki said.
The Palestinians began circulating a draft at the end of September after President Mahmud Abbas told the UN General Assembly that it was time to speed up the process of recognising Palestinian statehood.
Fabius's earlier met United States Secretary of State John Kerry, as well as British and German representatives.
Kerry has already vowed to veto the Palestinian resolution on the grounds that nothing should be imposed on Israel without bilateral discussions.
A European court on Wednesday ordered the Palestinian Islamic party Hamas to be removed from the EU’s list of terrorist organisation.
The 2001 listing of Hamas was based not on sound legal judgements but on "factual imputations derived from the press and the Internet," the General Court of the European Union said in a statement.
Both houses of the French parliament recently voted for the recognition of a Palestinian state, although the vote is not binding on the government.