Ehud Olmert, 62, resigned on Sunday amid corruption allegations.
Livni, aiming to become Israel's first female prime minister since the 1970s, is expected to be asked by President Shimon Peres to form a new government later on Monday, and will have 42 days to do so and avoid early parliamentary elections.
The Haaretz newspaper said Livni, who replaced Olmert as leader of the ruling Kadima party last Wednesday, met with Defense Minister Ehud Barak, who heads the Labor party. Livni's aides described the negotiations as "good", and Livni assured the Labor leader that he would be a "full partner" in her planned government, the paper said.
The meeting came amid reports that Barak may seek a coalition deal with former premier Benjamin Netanyahu, the leader of the right-wing opposition Likud party, which has called for an early election.
The 50-year-old foreign minister, a trained lawyer and former Mossad spy, faces an uphill struggle to bring the ultra-Orthodox Shas party into the coalition. The party has demanded extra budget funds to help low-income Israelis, and has pledged to quit any governing coalition if the issue of Jerusalem's status is raised at Israeli-Palestinian peace talks.
Olmert had first announced his intention to resign on July 30, as pressure mounted over a corruption probe. The premier faces criminal charges for allegedly accepting large bribes from a Jewish-American businessman. On September 6, police recommended that criminal charges should be brought against the premier.
Olmert, who succeeded Ariel Sharon in April 2006 after the former premier's stroke, saw his popularity plummet after the costly 2006 Israel-Lebanon war. While devastating Lebanon, Israel failed in its goal of preventing attacks from militant group Hezbollah.
A drawn-out leadership struggle in Israel would put under threat the goal of reaching a peace-deal with the Palestinians by January 2009. The target was agreed on at last November's U.S.-sponsored peace conference.
Two of the main issues blocking progress in Israeli-Palestinian talks are Jewish settlements in the West Bank and the future status of Jerusalem, with Palestinians seeking to reclaim east Jerusalem, seized by Israel in the 1967 Six Day War.
