Earlier, police named Hefetz as one of two Netanyahu associates under arrest for their suspected role in a separate wide-ranging corruption probe.
Netanyahu, who was the Communications Minister until 2017, is now not a suspect in this affair, according to the police, but local media widely reported that he is expected to be questioned in the recent days.
Police last week recommended Netanyahu be charged with bribery and breach of trust in two other cases.
Netanyahu has denied wrongdoing in those cases.
Hayut was said to have been informed in real time of an alleged 2015 offer by a former spokesperson for the Netanyahu family, Nir Hefetz, to appoint a fellow judge as attorney general if she agreed to halt an investigation into the prime minister's wife Sara, according to Hebrew media reports.
The new allegations significantly raise the level of political and legal peril he faces, suggesting that Mr. Netanyahu or his camp could be exposed to obstruction of justice charges.
The rightwing leader, in office for 12 years since 1996, has seen his dominance of Israeli politics threatened by corruption investigations since police recommended a week ago that he be indicted for bribery and fraud.
Five people were detained on suspicion of trading favours in a fresh corruption investigation into Israel's largest telecommunications company, the Israel Securities Authority said in a statement on Sunday.
A spokesman for Netanyahu said that "Hefetz never presented this ridiculous proposal to the prime minister and his wife, and was never asked by them to make such a proposal, and we don't think he even considered such a thing". Elovitch is a family friend of the Netanyahus.
Bezeq's main shareholder, Shaul Elovitch, was also arrested, along with his wife and son, and Bezeq's CEO Stella Handler. In return, police say Netanyahu had operated on Milchan's behalf on USA visa matters, legislated a tax break and connected him with an Indian businessman.
In return for the goods, Netanyahu allegedly helped Milchan to protect his investments in the Israeli media, including Channel 10 TV.
Israeli media previously reported that the Israeli news site Walla!, owned by Elovitch, is suspected of exchanging favors for favorable news coverage for the premier, a similar arrangement to a previous and still ongoing investigation with another Israeli news site known as Case 2000. While Netanyahu has not been named as a suspect, close associates of his, including two personal aides, have been arrested or questioned.
In the second case, Netanyahu is accused of offering to give preferential treatment to a newspaper publisher in exchange for favorable coverage.