Al-Umari said Tzipi Livni, the Israeli foreign minister, may assume the post of prime minister until the investigation is completed.
"The [foreign] minister will replace him and can keep the job for 100 days. After that the president of Israel nominates people to form a new government by preparing for elections," said al-Umari.
Early elections could be held possibly in November to choose a new prime minister.
Police have interrogated Shula Zaken, a director in Olmert's office, for the fourth time. She is currently under house arrest, al-Umari said.
"It seems that Olmert is in a very embarrassing situation. Stepping down is now a matter of time."
The Israeli media have not reported the latest developments in the case, but The New York Post newspaper has carried a story on the alleged bribery scandal, al-Umari said.
Some sources believe that Olmert is being targeted by a right-wing religious group which used to back him when he was with the Likud party as a right-wing activist.
This group, they say, is believed to be pursuing the case in view of possible progress in negotiations with the Palestinians, al-Umari said.