Abbas and Hamdallah met Friday at the president's home and are scheduled to meet again Saturday, at which time Hamdallah is to make a final decision, Haaretz reported.
Hamdallah announced his resignation Thursday following a dispute between himself and deputies Mohammed Mustafa and Ziad Abu Amru, who also serve as advisers to the president.
Hamdallah took office June 2, succeeding Salam Fayyad, who stepped down after feuding with Abbas. At the time of his appointment, Hamdallah said he planned to serve until mid-August.
Officials within Abbas' office told Haaretz that the president was angry Hamdallah resigned and did not inform him of his decision before making a public announcement.
"There is a feeling here that Abu Mazen [Abbas] is very angry with this move but has not yet decided whether to accept the resignation, once again embarking on choosing from a mix of possible names and all the speculations about the next prime minister, or whether to sort out the issues with the prime minister and his deputies," the official said.