Favours for funds
Authorities are trying to establish whether Olmert dispensed favours in exchange for funds before he became prime minister in 2006.
The case could force Olmert from office and hamper US-backed peace talks between Israel and the Palestinians.
Al Jazeera's David Chater, reporting from Jerusalem, said: "Police are already talking about a fourth round of interrogations."
"What they're looking at right now [is] an indictment for bribery."
Olmert says he did nothing wrong in his dealings with Morris Talansky, a New York-based Jewish fundraiser, but has promised to step down if indicted.
In testimony on May 27, Talansky told the Jerusalem District Court that he had passed $150,000 to Olmert over a 15-year period, including loans that were never repaid.
Talansky said some of those funds were spent on expensive cigars, hotels and other extravagances.
Olmert says the money was used legally to fund election campaigns.
His lawyers plan to cross-examine Talansky starting on July 17 in court hearings expected to last several days.
The allegations have stirred new calls for Olmert's resignation - and for early elections to be held - from within his Kadima party and its Labour allies.
Olmert averted a coalition crisis over the affair when he agreed to hold a party leadership election.
On Thursday, the Kadima party confirmed that it would hold a leadership election in September.
Tzipi Livni, Olmert's deputy and foreign minister, appears favoured to win, a survey from Israel's Yediot Aharonot showed on Friday.
Shaul Mofaz, Israel's transport minister, and Avi Dichter, the public security minister, are also in the running, although it remains unclear whether Olmert himself will seek to run again.