Olmert, who could face criminal indictment in corruption probes, submitted his resignation to Peres on Sunday, four days after he was replaced by Foreign Minister Tzipi Livni as leader of the ruling Kadima party in an internal election.
Israel's president was expected to ask Foreign Minister Tzipi Livni on Monday to form a new government before he heads to New York for the UN General Assembly.
"(Peres) is meeting with many factions today, and something might change, so I can't say for sure he will choose Tzipi Livni, but that's how it's looking," Peres spokeswoman Ayelet Frish told Army Radio.
Livni, 50, is hoping to become the second woman prime minister in the nation's history after "iron lady" Golda Meir, who served from 1969 to 1974.
If Livni, Israel's chief negotiator in peace talks with the Palestinians, gets the nod she will have up to 42 days to try to put together a coalition in order to avert snap elections, otherwise not due until 2010.
But in the rough and tumble of shifting allegiances in the Israeli political scene, there is no guarantee Livni will be able to come up with the numbers to form a coalition government and avoid an early election.
Livni, a former Mossad spy, also faces tough challenges in seeking to unify Kadima after new rifts emerged in the wake of her narrow victory over Transport Minister and former army chief Shaul Mofaz.
Formed less than three years ago, the centrist party itself has been dogged by allegations of corruption.
The continuing political turmoil in Israel has cast a shadow over peace talks with the Palestinians which were revived only in November, further denting hopes of a deal by the end of this year.
Both sides remain deeply divided on core issues, including final borders, Jewish settlements in the West Bank, the fate of 4.6 million Palestinian refugees and the future status of Jerusalem.
The ultra-Orthodox party Shas’ refusal to negotiate the fate of Jerusalem could prove particularly tough for Livni, who is currently the lead negotiator for Israel.
The Palestinians want mostly Arab east Jerusalem, which Israel seized in the 1967 Six Day War, as the capital of their future state. Israel, however, considers the entire city to be its "eternal, undivided" capital, a claim not recognized by the international community.
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