Israel has confirmed that there has been slight progress in talks for a prisoner swap, Israel Hayom reported.
At the same time, the report added that there have, as yet, been no breakthroughs.
Egypt and Qatar are working in parallel to create a deal, as Israel hopes that one of the two will see success.
According to the report, it is estimated that such a deal will take time, though if Hamas becomes significantly more flexible, things could progress quickly.
Meanwhile, the War Cabinet is expected to meet Sunday to discuss the possibility of a prisoner swap, as well as the question of what "the day after" the war ends will bring.
According to Kan 11 News, the War Cabinet has given a green light to Mossad chief David Barnea to move forward with the Qatari proposal, which would see dozens of hostages freed in exchange for a lengthy break from the war - but not a permanent ceasefire.
On Friday evening, Kan 11 News reported that Barnea on Thursday passed on a message from Qatar to the War Cabinet, stating that Hamas no longer insists on ending the war as a condition for moving forward with a new hostage release deal.
According to a source with knowledge of the details, the discussion is now focusing on a humanitarian deal, but the prices that Israel will have to pay in terms of days of respite and the release of prisoners will be "heavier."
Meanwhile, Channel 12 News reported that the Qatari proposal, still in the preliminary stages, would during the first stage include the release of 40-50 hostages, in exchange for a complete ceasefire of one month. The second phase is expected to be more complex and its details are not yet clear, but the assessment is that it would include an arrangement for the IDF's withdrawal from the Gaza Strip.
An Egyptian proposal would include a first stage in which Israel will stop the fighting for at least two or three weeks, and Hamas would release 40 hostages in return for 120 terrorists. In the second stage, a professional government will be established in the Gaza Strip consisting of Hamas and Fatah members, and the bodies of IDF soldiers will be released.
In the third stage, Israel will announce the end of the war, the IDF will leave the Gaza Strip, and the terror organizations will release the remaining hostages.
A Hamas delegation was due in Cairo on Friday to give its "observations" about the Egyptian plan.