The proposal suggests Hamas release five Israeli hostages each week, sources said.
A security delegation from Egypt has left for Qatar for talks, which will include increasing aid to the enclave and releasing remaining hostages, state-affiliated al-Qahera News TV said on Thursday.
Violence has escalated in the Gaza Strip since a January truce broke down on March 18 after two months of relative calm.
Asked about the latest proposal, a Palestinian official close to the mediation efforts said "there are some offers that look better than the previous ones".
When asked if he expects an announcement on a breakthrough on Thursday, he replied: "Maybe not yet".
There was no immediate response from Israeli Prime Minister Benjamin Netanyahu's office on the proposal but a spokesperson said there is currently no Israeli delegation in Doha.
Israel and Hamas accused each other of breaching the truce, which had offered respite from war for the 2.3 million inhabitants of the Gaza Strip which has been reduced to rubble.
Hamas, which still holds 59 of more than 250 hostages Israel says the group seized in its October 7, 2023 attack, accuses Israel of jeopardising efforts by mediators to negotiate a permanent deal to end the fighting.
Israel says it would be willing to extend the ceasefire temporarily if Hamas releases more hostages but without moving yet to a second phase during which it would negotiate a permanent end to the war.
Israel also said it won't accept Hamas' presence in the enclave and added it wanted to extend the ceasefire's temporary first phase, a proposal backed by US envoy Steve Witkoff
More than 50,000 Palestinians have been killed in the fighting, Gaza health officials say.
Hamas spokesman Abdel-Latif Al-Qanoua was killed in an Israeli air strike in the north of the Gaza Strip, Hamas-affiliated media said early on Thursday.
Qanoua was killed when his tent was targeted in Jabalia, the Hamas-run al-Aqsa television said.Â
The same strike wounded several people while separate attacks killed at least six in Gaza City and one in southern Gaza's Khan Younis, medical sources said.
Later on Thursday, the Israeli military confirmed in a statement that it killed Qanoua, saying that "he served as one of Hamas' key inciters".
Earlier this week, Israel killed Ismail Barhoum, a member of Hamas' political office, and Salah al-Bardaweel, another senior leader.
Both Bardaweel and Barhoum were members of the 20-member Hamas decision-making body, the political office, 11 of whom have been killed since the start of the war in late 2023, according to Hamas sources.
