In July, the attorney general, Avichai Mandelblit, said he had given the go-ahead for inquiries into a "matter" involving Netanyahu, defining the case as "an examination and not a criminal investigation into the prime minister".
Israeli media said it concerned suspicions of fraud and money laundering against Netanyahu's former chief of staff, Ari Harrow.
Mandelblit, who was appointed attorney general in February after serving for three years as Netanyahu's cabinet secretary, has been accused by some media of dragging his feet over the case.
"No one has an interest in delaying the probe. No one derives any benefit from it being delayed," he said.
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"If reasonable suspicion comes to light, it will turn into a criminal investigation - and I don't care who the subject is."
At this stage that is not the case, Mandelblit said, "but the examination is still not over, and changes are always a possibility".
According to Haaretz newspaper, Harrow was suspected of involvement in the fictitious sale of a business supposedly worth USD 3 million.
In June, he acknowledged receiving money from French tycoon Arnaud Mimran, who was sentenced to eight years in jail over a USD 315-million scam involving the trade of carbon emissions permits and the taxes on them.
In May, Israel's state comptroller released a critical report about Netanyahu's foreign trips, some with his wife and children, between 2003 and 2005 when he was finance minister.