Israel's attorney general wants to try Olmert for alleged double billing of Jewish groups for trips abroad.
Olmert said in July that he would step down as prime minister and not contest parliamentary elections scheduled for February, to fight corruption allegations. He is currently head of a caretaker government
However, Livni has said that he should not wait untill the elections to resign.
His exit would allow Livni to become acting prime minister until the elections.
Livni became leader of the Kadima party in September after an internal election.
But she was unable to gather support of enough legislators to form a new ruling coalition, prompting February's early vote.