Prime Minister Benjamin Netanyahu is interested in passing a law in the next Knesset session that will prohibit the recording of conversations without the permission of all participants.
Israel currently allows the recording of a conversation by one of the sides without the consent or notification of other side. Both police and journalists are concerned that such a law could impede criminal investigations and investigative journalism.
Mr Netanyahu has not made any official announcement on the subject or tabled a legislative proposal but referred to a possible anti-recording law in a ministerial committee meeting last week.
A proposal for such a law was blocked by former attorney-general Yehuda Weinstein two years ago.
Sources close to the prime minister have said that his intention is to "safeguard the right to privacy", but his critics claim that it is mainly aimed at preventing damaging evidence of his personal and family affairs from seeing the light of day.
It is expected that under such a law, police investigators would be exempt and still allowed to record suspects. However, in many criminal cases, crucial evidence is obtained by private citizens who have recorded their conversations with suspects. The same, of course, is true of work done by investigative journalists.
Zionist Union MK Ksenia Svetlova, who chairs the Knesset freedom of speech and press lobby, said that such a law would "prevent journalists from carrying out investigations and revealing the truth. This is coming from a prime minister who is also fighting the media".
Former prime minister Ehud Olmert, who is currently serving a 19-month prison term for bribe-taking, was also indicted for the obstruction of justice on the basis of recordings of conversations made by his former secretary, Shula Zaken. Members of Mr Netanyahu's Likud Party have recently proposed that serving prime ministers be shielded from police investigations during their term of office.