Police and Netanyahu's office declined to comment on the reports.
Various Israeli media reports said investigators arrived at Netanyahu's residence in central Jerusalem in the afternoon for a second round of questioning.
Netanyahu is suspected of receiving gifts from business people, according to Attorney General Avichai Mandelblit, who is overseeing the investigation. He has provided few other details.
Israeli media reports say he allegedly received tens of thousands of dollars in such gifts.
The probe has shaken the country's political scene and raised questions over whether Netanyahu, 67 and in his fourth term as prime minister, would eventually be forced to resign.
US billionaire and World Jewish Congress president Ronald Lauder has been among those questioned in the probe over gifts he allegedly gave Netanyahu and alleged spending on trips for him, reports have said.
Lauder, whose family founded the Estee Lauder cosmetics giant, has long been seen as an ally of Netanyahu.
Netanyahu has also acknowledged receiving money from French tycoon Arnaud Mimran, who was sentenced to eight years in prison in France over a scam involving the trade of carbon emissions permits and taxes on them.
Netanyahu has denied any wrongdoing, saying repeatedly that "there will be nothing because there is nothing".
The inquiry has led to fierce debate in Israeli politics, with Netanyahu's allies accusing opposition politicians and some in the media of unfairly pressuring the attorney general.
Others have accused Mandelblit of moving too slowly in the intensely watched probe.
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