Israeli investigators are looking into allegations that Olmert accepted cash payments from an American businessman and double-claimed expenses for trips before he became prime minister.
The winning candidate in the Kadima race must win at least 40 per cent to take the chairmanship. Otherwise, those with the two highest number of votes will contest a runoff.
Once Olmert steps down, the new Kadima leader will have 42 days to assemble a 61-MP majority in the 120-member Knesset.
National elections will be held within three months if the Kadima chairman fails to win the requisite support from parliament.
|Mofaz, left, is looking to replace the
scandal-hit Olmert [AFP]
Kadima is trailing the Likud party of Benjamin Netanyahu, a former Israeli prime minister, in opinion polls, suggesting that forming an assembly will be tough for the Kadima leader.
Yehezkel Dror, a political analyst, said: "The problem is not what is happening at Kadima but what will happen in the next
elections ... we cannot predict how Netanyahu would behave if elected."
A survey among Kadima members on Monday predicted Livni would win 48 per cent of the vote and Mofaz 28 per cent. The other two ministers contesting the leadership - Avi Dichter, the internal security minister, and Meir Sheetrit, the interior minister - are far behind.
Livni, 50, advocates an Israeli withdrawal from most of the occupied West Bank and east Jerusalem in order to reach a two-state solution with the Palestinians.
"I want to hold peace negotiations as long as the Palestinians want the same. But any agreement must provide security to Israel," she told supporters recently.
Mofaz, 59, a former army chief of staff and defence minister, says he will not offer increased support to Mahmoud Abbas, the Palestinian president and leader of Fatah, as long as Hamas controls the Gaza Strip.
Hamas forces routed their Fatah opponents in the Gaza Strip in June 2007.
"Negotiations should be held from a position of strength and not out of weakness or lack of choice," Mofaz said recently.
"We should move forward in a manner that will guarantee Israel's security in any future reality and not hurry to give up strategic assets with nothing in return."
Mofaz has also said in the past that if he were in power, he would not rule out an attack on Iran over its alleged nuclear weapons programme. Tehran denies its uranium enrichment programme is geared towards making a nuclear bomb.
Mofaz has sought to emphasise his experience in security matters, while Livni has said that "generals should not have a monopoly over Israel's security".
Kadima made the strongest showing in February 2006 elections just months after it was founded.
But corruption scandals and criticism of the government's handling of Israel's 34-day war in Lebanon in 2006 have undermined its rule.