Israel and the Islamic group Hamas continue their negotiations for a ceasefire in Gaza and the release of the remaining hostages seized by the group last year.
The two sides have been engaging in talks mediated by Egypt and other parties.
Hamas said on Saturday that it received the Israeli proposal and will examine its contents.
US news website Axios reported that the proposal includes "a willingness to discuss the 'restoration of sustainable calm' in Gaza after an initial release of hostages on humanitarian grounds."
Axios said the proposal marks the first time that Israel has suggested it is open to discussing an end to the conflict in Gaza.
The development came as Israel is reported to be preparing to launch a ground operation in the southern Gaza city of Rafah, where about 1.2 million people are staying.
Israeli Foreign Minister Israel Katz told a local TV station on Saturday that the release of the hostages is the top priority. He also said that if there is a deal, the government would suspend its operation.
Hamas released on Saturday a video showing two male Israeli hostages who urged their government to be flexible in responding to the group's requests.
Meanwhile, hot temperatures in Gaza have reportedly caused fatalities, including children.
Many displaced people are living in tents without cooling fans. Their health conditions could worsen as summer approaches.