Israel has offered Hamas, through Qatari and Egyptian mediators, a pause in fighting for up to two months as part of a deal to release all hostages, US news site Axios reported.
The report, which cited unnamed Israeli officials, said the deal would take place in several stages, the first of which would see the release of women, men over 60 and those in critical health.
The next stages will include the release of female soldiers, younger male civilians, male soldiers and the bodies of dead hostages.
Officials said the deal would also lead to the release of an as yet unspecified number of Palestinian prisoners held in Israel, but not all.
The proposal does not include promises to end the war, but would include reducing the presence of Israeli troops in major Gaza cities and gradually allowing residents to return to the territory's devastated north.
Officials said the agreement is expected to take about two months to implement.
Israeli media outlet Ynet also reported the proposal, citing unnamed sources, and said Prime Minister Benjamin Netanyahu had hinted at it during a meeting with the families of the hostages on Monday.
News of the proposal comes as US media reported that White House Middle East coordinator Brett McGurk was due to arrive in the region for meetings in Egypt and Qatar aimed at hammering out a new hostage exchange deal. /BGNES