Earlier, Israel's chief prosecutor had said that investigators suspected Olmert had taken envelopes of cash from Talansky, a New York based fundraiser.
Israeli police say no charges have been filed against Olmert.
"Detectives and state prosecutors are exploring the possibility that he took bribes, violated campaign funding laws and laundered money," police said.
Olmert has acknowledged taking money from Talansky for political campaigns, but said his campaign finances were the responsibility of a longtime confidant.
Olmert's confidant was also separately questioned by the police on Thursday.
Meanwhile, Talansky has said that he received nothing from Olmert in exchange for the money. He is due to give evidence in court on Sunday.
Prosecutors want Talansky to give evidence under oath before a court order banning him from leaving Israel expires on Monday.
Jacques Chen, Talansky's lawyer, said: "He is anxious to return to the US immediately thereafter."
Olmert's defence team, however, wants to put off Talansky's testimony, saying it needs more time to prepare for his cross-examination.
Israel announced on Wednesday that it had begun indirect peace talks with Syria in Turkey, a move that many Israelis think is meant only to divert attention from the inquiry into Olmert.