Police reportedly have a copy of a recording made by Harrow of a 2014 conversation between Netanyahu and the publisher.
Netanyahu's predecessor, Ehud Olmert, was released from prison last month after serving a 16-month sentence.
The Channel 10 survey comes after police revealed or the first time that investigations of Netanyahu revolve around suspicions of "bribery, fraud and breach of trust". Harow is expected to receive six months of community service and a $193,000 fine on breach of trust charges in exchange for his testimony.
In 2003, he staged a comeback, and served for two years as finance minister, only to have it surface after the 2009 victory that heralded his current terms as prime minister that he and his family had accepted expensive vacations and dinners at the expense of well-heeled businessmen; the obvious implication was that there would be some quid for that quo.
Netanyahu has repeatedly denied wrongdoing and calls the accusations a witch hunt. "We reject outright the unfounded claims", the spokesman said.
"The campaign to change the government is underway, but it is destined to fail, for a simple reason: there won't be anything because there was nothing".
Two of the key protagonists rallying against Netanyahu at Saturday night's demonstration included political activist Daphni Leef, one of the main organizers of the Israeli social protests that erupted in the summer of 2011, and Meni Naftali, the former chief caretaker at the prime minister's residence, who successfully sued the Netanyahu family for being mistreated during his employment.
Even if eventually indicted, Netanyahu would not be obliged by law to resign.
Israeli Prime Minister Benjamin Netanyahu attends the weekly cabinet meeting at his office in Jerusalem, Israel, Sunday, Jan. 29, 2017.
She added that coalition partners would discuss the ethical ramifications of such a development but that it was still premature.