Police said they have established an evidentiary foundation to charge the pair with accepting bribes, fraud and breach of trust.
Police recommended that charges also be brought against Elovitch and his wife.
Police also recommended indicting Mr Elovitch and his wife Iris for giving bribes, among other offences, while the statement said their son Or should face fraud charges.
Authorities claim Mr Netanyahu awarded regulatory favours to the country's leading telecommunications company, Bezeq Telecom Israel, in return for more favourable coverage of him and his wife on its news website, Walla.
The prime minister has denied any wrongdoing, dismissing the accusations as a witch hunt orchestrated by the media.
In Case 1000, Netanyahu is suspected of having received gifts from businessmen overseas totaling 1 million shekels (approximately $280,000), including cigars, champagne, jewelry and more, from 2007 through 2016.
The recommendation of an indictment against the prime minister for the third time this year prompted calls for his resignation.
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According to messages exchanged that day between Elovitch and Yeshua, Hefetz had told Elovitch that the prime minister's staff believed the two investigations concerned Elovitch and Netanyahu's relationship with Australian billionaire James Packer.
The head of the opposition Labour party, Mr Avi Gabbay, renewed his call for Mr Netanyahu to resign after the latest recommendations were released.
A year after that tense meeting, in December 2017, as part of his testimony in a separate graft case over allegations Elovitch had defrauded investors, Yeshua would hand his phone over to police, knowing full well what it contained and, say investigators, with great relief at being rid of it.
Netanyahu has rejected the allegations, saying: "These recommendations were determined and leaked even before the investigations began".
That act launched what is today known as Case 4000. The attorney general will make the final decision on whether to press charges.
"A prime minister with so many criminal cases around him can not continue in his job and must resign", said Avi Gabbay, the head of the Labor party. "A person with such a sickly obsession with what the media says about him must not lead the State of Israel".
"The question is what will happen first: Will the attorney-general decide to prosecute or will the Government collapse?" said Reuven Hazan, a professor of political science at Hebrew University of Jerusalem.