According to the report, the two leaders agreed to open a secret channel to discuss the issues, which include such sticking points as refugees, Jerusalem, and final borders, during their meeting roughly two weeks ago.
The report stated that the talks have yet to produce a breakthrough.
Olmert confirmed last week that he intends to engage in negotiations with Abbas on the formation of a Palestinian state.
Olmert was responding to a Haaretz report, according to which he offered to hold negotiations toward an "Agreement of Principles" for the establishment of a Palestinian state comprised of the Gaza Strip and most of the West Bank.
Olmert's proposal to Abbas is based on his view that it is important to first discuss issues that are relatively easy for the two sides to agree upon. The prime minister also believes that such an accord will enjoy the overwhelming support of the Israeli public and the Knesset.
Abbas, however, told Meretz Chairman Yossi Beilin during their meeting in Ramallah last week that an agreement of principles would not be satisfactory. He said the Palestinian Authority is prepared to achieve a final status settlement with Israel by next fall, when an international Mideast peace conference is scheduled to take place.