The prime minister also plans to appoint former minister Haim Ramon vice premier and a minister without portfolio.
While the Prime Minister's Office has yet to issue an official statement in the appointment, Olmert's aides confirmed that Bar-On was the leading candidate for the post.
"The decision on the reshuffle will be taken by the prime minister tomorrow," the aides said.
Meir Sheetrit, the current housing minister, will replace Bar-On in the Interior Ministry, and Jacob Edery will be appointed the new housing minister.
Suspended Finance Minister Abraham Hirchson submitted his letter of resignation over the weekend.
The resignation will go into effect within the next 48 hours.
Hirchson is being investigated over suspicions that he embezzled funds from the non-profit Nili organization (associated with the National Workers' Organization) while he headed the workers' association.