Hamdallah "presented his resignation in writing to the president following disagreements with his two deputies," the official told AFP, speaking on condition of anonymity.
A separate government source confirmed Hamdallah had presented his resignation, citing a "power struggle".
It was not immediately clear whether Abbas was likely to accept the resignation of the highly respected academic who was named to the position on June 2 following the resignation of former premier Salam Fayyad.
A new government under Hamdallah's leadership was sworn in on June 6, which included two deputy prime ministers, Ziad Abu Amr and Mohammed Mustafa.
Fayyad himself resigned in mid-April after months of difficult relations with Abbas which hit a crisis over the resignation of finance minister Nabil Qassis, which the premier accepted but the president did not.
Mustafa, who heads the Palestine Investment Fund, was tipped as a possible successor to Fayyad.