The new investigation stemmed from a separate probe into alleged bribery in the form of positive news coverage of Netanyahu in return for business concessions worth millions made public just hours earlier.
The revelations come just days after police said there were grounds to indict the prime minister himself in a separate case for bribery, fraud and breach of public trust, in the biggest challenge yet to the right-wing premier's long tenure in power.
A statement from the police said two men had in 2015 "approached a public official with an offer to help advance her to the position of attorney general" in return for her taking certain action "on a criminal case," with the offer never reaching fruition.
The two men have been identified as Nir Hefetz and Eli Kamir, both former media advisers for the Netanyahu family.
Their alleged offer was to Hila Gerstel, a judge involved in a graft probe into Sara Netanyahu over alleged misuse of public funds.
A spokesman for Netanyahu said that "Hefetz never presented this ridiculous proposal to the prime minister and his wife, and was never asked by them to make such a proposal, and we don't think he even considered such a thing."
Police have already concluded investigations into two separate cases involving the prime minister and their recommendation that charges be pressed is now in the hands of the attorney general.
Tuesday's revelations came as police commissioner Roni Alsheich faced a parliamentary committee after outrage among lawmakers over a recent interview, in which he said that detectives probing Netanyahu had been targeted by private investigators to dig up dirt on them.
Left-wing lawmakers accused the committee, headed by Yoav Kish of Netanyahu's Likud party, of trying to "terrorise" Alsheich to sway the outcomes of police work on suspicions connected to Netanyahu.
Supporters of the premier said Alsheich's interview with Israel's Channel 2 television further weakened the public's trust in the police, perceived by some as attempting to frame Netanyahu.
"I didn't mention the prime minister in connection with anything, I said that there were persons sniffing around the investigators working on these cases," Alsheich told committee members, several of whom admitted not having seen the broadcast.
The latest suspicions emerged from a corruption probe involving Hefetz, who on Sunday was arrested along with another Netanyahu associate Shlomo Filber.
Also arrested were Shaul Elovitch, the controlling shareholder of telecommunications group Bezeq, as well as members of his family and senior Bezeq executives.
Police suspect Elovitch was granted business concessions in return for Netanyahu receiving positive coverage on Walla!, a news website he owns.
Hefetz and Filber are suspected of passing Netanyahu's wishes and demands to Bezeq and Walla! officials.
"As part of the investigation, suspicions accumulated of felonies concerning ethics, fraud, money-laundering and securities violations, conducted over extended periods of time, frequently and systematically as part of relationships between Bezeq executives and public servants and their associates," Tuesday's police statement said.
Elovitch has already been investigated over a merger of Bezeq with cable company Yes which saw him pocketing dozens of millions of dollars.
Netanyahu has not been named as a suspect in the Bezeq affair, but a spokesman for his family responded to media reports on the investigation, calling them "yet another empty probe" that would yield nothing.
This would not be the first time that Netanyahu has been accused of trying to win good press in corrupt ways, as police believe the premier sought a secret deal for favourable coverage with the publisher of top-selling newspaper Yediot Aharonot, whose publisher Arnon Moses could also face bribery charges.
The attorney general must now decide how to move forward with the police recommendations on the Yediot Aharonot affair and another case involving gifts from Hollywood producer Arnon Milchan and Australian billionaire James Packer, in a process that could take months.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)