Barak revealed to his advisers that he was "disgusted" by Olmert's actions as described by Talansky, Israel Radio said.
Barak at the very least is expected to say Olmert acted improperly.
He will also probably call on Olmert to step down for the duration of the case, Israel Radio reported.
He could also suggest that Olmert's Kadima Party find another leader, according to the report.
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said that Barak might pull his party out of the coalition government.
"Barak's Labour party has 19 seats in the Knesset - it's the key coaltion partner - if Ehud Barak was to pull out of the coalition then Olmert's government would fall," she said.
Barak will say Olmert has been morally tainted by the testimony, Hanan Crystal, a commentator, told Israel Radio.
Barak could start a process that could bring Olmert's downfall, Ayala Hasson, another analyst, told the radio.
|Barak, left, may ask Olmert's Kadima to find|
another leader for the case's duration [AFP]
"From all this mess it's clear we're going to elections," Hasson said.
Barak's spokesman did not immediately return a call requesting comment.
The political fallout came after Talansky told an Israeli court on Tuesday of cash payments totalling $150,000 that he transferred to Olmert over a 15-year period ending in the mid-2000s.
He told the court of Olmert's love for luxury hotels, fine cigars and first-class travel and said he overlooked doubts about Olmert's request for cash due to his belief in Olmert's ability to unite the Jewish people.
Police suspect Olmert accepted illegal campaign contributions or bribes.
Talansky said an attempt by Olmert to get three businesspeople to work with a company owned by Talansky failed.
Olmert has denied wrongdoing and said he will resign if charged.
The court took Talansky's deposition prior to any filing of charges against Olmert since the prosecution feared Talansky would return to the US and refuse to return.
Talansky has said he will agree to come back, and is expected to be cross-examined by Olmert's lawyers on July 17.
Olmert's downfall or any preoccupation with defending himself could severely hamper the US-backed efforts to work out a final peace deal with the Palestinians by the end of the year, as well as recently renewed negotiations with Syria.