The revelations came during a court hearing in which it was disclosed that prosecutors are negotiating with a former senior aide to Netanyahu, the Haaretz newspaper said.
They are said to be trying to obtain testimony from ex-chief of staff Ari Harow about two cases relating to gifts allegedly given to Netanyahu and his family by business figures and discussions he had with a newspaper publisher.
The prime minister was questioned earlier this year under caution by police over the allegations.
Netanyahu has denied the claims. In a statement, his office said: “We completely reject the unfounded claims made against the prime minister.
“The campaign to change the government is underway, but it is destined to fail, for a simple reason: there won't be anything because there was nothing.”
If Harow gives evidence against his former boss, it would increase the chances of Netanyahu facing charges.
Although he would not be forced to resign if indicted, it would increase pressure on him to step down after 11 years in office.
One investigation, known as Case 1,000, involves Hollywood producer Arnon Milchan, who was allegedly asked to purchase luxury items for Netanyahu and his wife.
Case 2,000 relates to claims of a proposed deal for more favorable coverage with Arnon Mozes, the publisher the Yedioth Ahronoth newspaper.
The details of the inquiries were included in a document submitted to Rishon Lezion Magistrate’s Court, which ordered a media gag on the details of prosecutors’ negotiations with Harow.
The order said the cases related to the “suspicion of the commission of the felonies of bribery, fraud and breach of trust”.
Harow was Netanyahu’s chief of staff in 2008 when he was opposition leader. He returned to work with the prime minister in 2014 but resigned a year later amid corruption claims.