The meeting which will start at 0800 GMT was scheduled after US Secretary of State John Kerry asked Abbas in a telephone conversation late Friday to find common ground, the source said.
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Rumors Fayyad, a US-educated economist, would either resign or be told to step down by Abbas have been rife in recent weeks following the high-profile dispute between the pair over the government's hiring and firing policy.
Longstanding tensions between Fayyad and Abbas peaked on March 2 when the Palestinian finance minister, Nabil Qassis, announced he was standing down.
Abbas, who was abroad at the time, rejected the resignation but Fayyad agreed to it.
Last week, for the first time, the Fatah's Revolutionary Council openly criticized Fayyad's government over its economic policy.
The criticism came as several high-ranking officials suggested Abbas might be about to dismiss Fayyad.
Fayyad held the finance portfolio as well as the premiership before Qassis's appointment in May 2012.
Abbas's Palestinian Authority is in serious financial crisis, partly as a result of non-disbursement of promised foreign funding, although the US Congress quietly unblocked $500 million in aid last month.
According to a senior Palestinian official who spoke on condition of anonymity, Fayyad "has prepared his resignation since March 23" but it was put off because of US President Barack Obama's visit to the region and Abbas's overseas trips.
The United States on Thursday reacted warily to speculation Fayyad was poised to offer his resignation.
A senior official at the US State Department told reporters he did not believe Fayyad was on the verge of resigning.
"He's not tendering his resignation to the best of my knowledge. He's not doing it," the official said on the sidelines of G8 talks in London. "As far as I know he's sticking around."
A top State Department official later added: "We have no new information to suggest his resignation, but any confirmation of his plans would have to come from him or his team."
The international community gives Fayyad credit for building solid government institutions around the West Bank-based Palestinian Authority.
But he is considered by some in the Palestinian leadership to be too close to the United States.
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