Channel 10 TV has reported that Yair accepted free trips and other gifts from Australian billionaire James Packer.
Israeli police reportedly suspect that larger and more valuable presents were involved and Israeli media said the gifts may be worth "hundreds of thousands of shekels".
A spokesman for the Netanyahu family said: "All the supposed affairs will turn out to be fiction. We are repeating: there will be nothing, because there is nothing."
The police visit sparked a media frenzy in Israel and Netanyahu's aides erected black screens to stop waiting photographers from getting pictures of investigators arriving at the residence.
Netanyahu has so far weathered the political storm around the investigation. He began a Cabinet meeting by joking that political opponents thinking of buying new suits in case they are able to take his job should "call off their tailors".
Today he had another defiant message for the opposition, saying: "There will be nothing because there is nothing. You will continue to inflate hot air balloons and we will continue to lead the state of Israel."
The 67-year-old politician, who is on course to become Israel's longest-serving leader, has avoided prosecution at least twice so far in a long career.
During his first stint as Prime Minister in 1997 prosecutors opted not to charge him in a scandal over political appointments but said publicly that it was "a very difficult decision" not to indict him.
Three years later, police recommended charging both Netanyahu and his wife with illegally taking silverware, carpets and other items from the prime minister's residence when they moved out.
Prosecutors again decided not to bring charges, saying there was insufficient evidence.
Other political scandals involving Netanyahu and his family have ranged from the serious to the absurd.
He has been accused of a conflict of interest after it emerged that his personal lawyer was also working for a German company that supplies Israel's Navy with submarines. In 2013, Israeli media had a field day with reports that he was spending £1700 a year of taxpayer's money on ice cream.
Sara Netanyahu was questioned by police for nearly 12 hours in December for allegedly using state funds to pay for a caretaker for her father and for moving garden furniture out of the official prime minister's residence to the family's private home.
She denies any wrongdoing and no charges have been brought.
Police probes against politicians are common in Israel and Netanyahu's predecessor, Ehud Olmert, is in prison for corruption. Ariel Sharon was questioned by police over accusations he accepted bribes but the case was dropped and he was never charged.
- additional reporting AP
