Israel has accused Olmert of bribery - a criminal indictment, so it is clear he cannot be selected for the executive branch.
Israel's High Court has ruled that anyone indicted on a criminal charge cannot serve in the executive branch. He cannot be a minister, certainly not prime minister. That's why Aryeh Deri, Abraham Hirchson and Shlomo Benizri were forced to relinquish their positions as ministers. That's why Ehud Olmert had to resign as prime minister.