The deal would see a pause to hostilities in exchange for up to 40 vulnerable hostages, according to reports.
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Hundreds of Palestinian prisoners would also be released, some of whom have been convicted of killing Israelis.
A number of Palestinians will be allowed to return to northern Gaza, while humanitarian aid would be significantly increased.
Israel is set to send another delegation to Qatar to continue negotiating the final details this week, following a meeting in Paris over the weekend.
The meeting in Paris, which involved mediators from the US, Egypt and Qatar, dramatically boosted hopes for peace.
Officials claimed Hamas “dropped some of its demands” following pressure by prime minister Benjamin Netanyahu, but that the two sides were “still far from a deal”.
Mr Netanyahu said: “We are working to reach another framework for the release of our hostages, as well as the completion of the elimination of the Hamas battalions in Rafah.
“That is why I sent a delegation to Paris and tonight we will discuss the next steps in the negotiations.”
Hamas is yet to comment on the details of the proposal, but has previously said a ceasefire must be long-term and include a full withdrawal of Israeli troops from Gaza.
Israeli national security advisor Tzachi Hanegbi said a temporary ceasefire could “under no condition be interpreted as an end to the war”.
Of the 134 hostages held by Hamas in Gaza, some 50 are feared dead.
The Israeli army continued to strike both southern, central and northern Gaza over the weekend, with dozens of Palestinians killed.
It also announced it had arrested over 200 “terror suspects” at the Nasser hospital in southern Gaza in the past week.
Israel is gearing up to launch what could be a devastating ground invasion inside the refugee-filled Gazan city of Rafah.
Mr Netanyahu vowed to crush the “last bastion” of Hamas who he claims are hunkered down in the city to finally put an end to the grinding war.
The US hopes to oversee a ceasefire deal that would stop a ground invasion of Rafah, where up to 1.5million people are residing.
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