The source told Al-Araby Al-Jadeed that "despite the time constraints, the Hamas leadership abroad has succeeded in passing the latest Israeli response to the Hamas leadership in Gaza, through secured channels, which fulfilled its role in turn, in examining the proposal."
At the same time ,a diplomatic source reported that the Israeli delegation will not leave for Cairo on Tuesday, and instead wait for Hamas' response.
According to the Saudi-owned Al Arabiya, Hamas' response is expected to arrive on Wednesday evening.
The report said that Hamas leadership in Gaza send its response, with comments, back to Hamas leadership abroad, for the preparation of the final answer. The source added that Gaza's comments to Israel's response come not only from Hamas' leadership, but also from that of other Gaza terror groups, such as Islamic Jihad.
According to Al Akhbar, Egyptian officials in Cairo feel that the sides are closer than ever to reaching an agreement. The report added that Egypt is still convinced that there are matters which both sides will need to compromise on.
Egyptian sources also said that "additional changes have been made to the proposal in recent hours," and that "the goal is that there be as long a ceasefire as possible, which will ensure the complete end of the war, and not bring about its renewal once more." This, according to the report, would be backed by regional and international guarantees.
The newspaper said that Hamas is demanding that these guarantees be in writing, as part of the agreement, and that Israel sign them, since the terror group will not accept oral commitments.
The AWP news outlet on Tuesday morning quoted a source familiar with the details of the deal, saying that "the two sides are close and able to reach an agreement within a few days - if some of the issues which are disrupting this are quickly solved."
The source added that the Egyptian proposal is acceptable to both sides, but there are issues relating to the number of hostages to be freed. On this matter, Hamas has said in the past that it can identify only 20 elderly, female, and ailing hostages, while Israel is demanding 35-40 hostages.
"We can overcome this obstacle by means of a number of days of ceasefire which will be agreed-upon. What is suggested is six weeks, and it could be that this number will be reduced if Hamas does not agree to release more than 20 hostages," the source said.
Meanwhile, a Washington diplomat told Al-Araby Al-Jadeed that "the US government is pushing that a hostage deal and a ceasefire deal be part of a comprehensive plan, which will include normalization with two Arab states, and the return of the Palestinian Authority to Gaza. This is in addition to Egypt's cooperation in a security role in the region."
The diplomat added that Cairo "has confirmed to officials in the US government that it rejects all presence of non-Palestinian forces in Gaza, with the option of a full agreement for a temporary position with specific tasks, according to the request of the Palestinian leadership, on the condition that the character of the Egyptian role is advisory and not operational."