Police refused to confirm the reports. Netanyahu has already been questioned by police four times as part of the investigations.
Netanyahu is suspected to have received luxury gifts from wealthy supporters, including Israeli businessman and Hollywood producer Arnon Milchan, a longtime friend who reportedly sent boxes of expensive cigars and other items with a value of tens of thousands of dollars.
Milchan was again questioned in September.
The second affair over which Netanyahu has faced police questioning involves suspicions he sought a secret deal for favourable coverage with the publisher of top-selling daily Yediot Aharonot.
The alleged deal, not believed to have been finalised, would have seen Netanyahu receive positive coverage in return for helping curb Yediot's competitor, the pro-Netanyahu freesheet Israel Hayom.
Earlier in the week, Netanyahu confidants Yitzhak Molcho and David Shimron, partners in a law firm and both relatives of the premier, were questioned by police as part of a probe into suspected corruption around the purchase of German submarines.
Netanyahu himself has not been named as a suspect in the submarine case.
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