"The fourth round of questioning of PM Netanyahu has begun at his residence," Israel Hayom daily, considered close to the premier, reported on its website.
Public radio said that national fraud squad detectives arrived at the city centre house shortly before 5:00 pm (1500 GMT).
It said they were expected to interrogate him over suspicions of unlawfully receiving gifts from wealthy supporters, including Australian billionaire James Packer.
They would be looking for his response to testimony given by Israeli businessman and Hollywood producer Arnon Milchan, a friend of both Netanyahu and Packer.
More From This Section
Left-leaning daily Haaretz cited a police source as saying Netanyahu would also be asked to respond to testimony given by his wife that conflicts with his version of events.
Haaretz added that there would also be fresh questions about an alleged bid to strike a deal with an Israeli press baron.
Police refused to confirm or deny to AFP that the interview was taking place or to make any comment on the inquiry so far.
Netanyahu has repeatedly denied any wrongdoing.
Also being probed is a suspicion that the premier sought a secret deal with Amnon Moses, publisher of Israel's top-selling newspaper Yediot Aharonot.
The discussed deal, which is not believed to have been finalised, would have seen Netanyahu receive positive coverage in return for him helping scale down the operations of Israel Hayom newspaper, Yediot's competitor.
The investigations have stirred Israeli politics and led to speculation over whether Netanyahu will eventually be forced to step down.