The United States has promised to veto the application, which has been under review in the Security Council for over a month. But Washington hopes to avoid casting such a stop sign.
The State Department is counting on the Palestinian Authority move receiving less than the required nine votes for Security Council approval, making a U.S. veto unnecessary.
Diplomats say the unofficial head counts put the yes votes between eight and nine.
A closed series of consultations is scheduled to consider the issue during the first week of November.
Washington will press for more time to consider the application, but the Palestinians are under pressure at home to move the issue to a vote.
Last week, the confrontation between the Palestinians, the U.S. and Israel rose to the surface during a brief Security Council meeting on the regional situation in the Middle East.
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