It will be the first meeting between the two leaders since April, weeks before Hamas Islamists took over the Gaza Strip following months of violence with Abbas loyalists.
"The meeting will be held in Egypt next week," Abbas media adviser Nabil Amr said.
An official in Olmert's office said talks could take place, but added that no date had yet been set. Another senior Palestinian official said talks would be held in the Egyptian resort of Sharm El-Sheikh on Sunday.
"(They) will discuss the recent Palestinian developments as well as well as ways of reviving the peace process," said the official, who refused to be named.
Abbas sacked a Hamas-led unity government earlier this month following the Islamist group's takeover of Gaza and formed an emergency administration based in the West Bank city of Ramallah led by Prime Minister Salam Fayyad.
A planned meeting between the leaders in the West Bank that was due to take place weeks ago was cancelled amid the internal Palestinian strife, Palestinian rocket attacks and Israeli attacks against Gaza militants.
Israel and most of the West had shunned the Hamas-led administration but maintained dialogue with Abbas, a moderate.
After 15 months in which Israel shunned the Hamas-led cabinet, Israeli Foreign Minister Tzipi Livni's spokesman said she spoke to Fayyad on Tuesday, for a "beginning of a dialogue between the two governments".
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