The sources say the two will meet in order to prepare for another round of direct talks between Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas, which has not been scheduled yet.
Erekat is currently on a visit to New York, while Molcho is in Washington meeting with US officials. Netanyahu's office refused to comment on the report.
Meanwhile President Shimon Peres, speaking at the UN General Assembly in New York, was asked about the freeze on West Bank settlement construction, which is scheduled to end soon.
Peres said Netanyahu had imposed a 10-month moratorium on construction which, regrettably, had not been used for direct negotiations.
"Now the sides are searching for a creative solution," Peres said, adding that he was not surprised as he had experience in negotiations and that creative solutions were often necessary.
Earlier, Abbas said he does not mean to negotiate "for a single day" if Israel refuses to extend the freeze. Speaking en route to New York on Monday, Abbas stressed he was "not opposed to a settlement freeze for a month or two" and that it was possible "to conclude a peace deal on all final status issues if the settlement freeze is extended."
"If Israel stops the settlement and shows goodwill, then we can reach an agreement on borders and security, and agreement on other matters like the status of Jerusalem, water and settlements will follow" in due course, he told AFP.
The report said one of the Likud MKs presented the bill to Netanyahu two weeks ago, after he returned from Washington. The prime minister said he would consider it, and in the meantime a proposal was written up. Then, on Friday, he announced he would support the bill.
Ali Waked, Attila Somfalvi, and Yitzhak Benhorin contributed to this report
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