If no issues arise, a hostage deal could be signed by the end of this week, a Hamas official told the Saudi news outlet Asharq Al-Awsat.
The Wednesday report cited the official as stating that a deal was "imminent," with the main points having already been agreed upon.
According to Asharq Al-Awsat, in the first stage of the agreement, which is supposed to last some 45-60 days, Hamas would release some 30 hostages, both alive and deceased, in exchange for Palestinian prisoners.
In addition, IDF troops would withdraw from cities within the Gaza Strip.
However, they would remain in the Philadelphi and Netazrim corridors. These corridors run parallel to the border with Egypt and cut across central Gaza, respectively.
Palestinian women and children would be allowed to return to northern Gaza.
On Tuesday, officials with knowledge of the negotiations told The Jerusalem Post that a hostage deal could be achieved within a month, with significant advances being made.
Hostage deal reportedly 'closer than ever'
This follows a Tuesday Washington Post report, citing a Hamas official, which claimed the terror group had ceded its demands that the war ends and that Israeli troops withdraw from the Gaza Strip in the framework of a hostage deal.
"There is a noticeable shift in public opinion,” a Hamas member was quoted as saying by the publication, adding, “There is now a strong desire to end the war at any cost.”
On Monday, Defense Minister Israel Katz said a hostage deal was closer than ever.
Such a remark was reiterated by a senior Hamas official, cited in the Saudi news outlet Asharq Al-Awsat.
“We are closer than ever to reaching a prisoner exchange deal and a ceasefire, provided that Netanyahu does not obstruct the agreement,” he reportedly said.
Amichai Stein, Sam Halpern and Raquel Guertzenstein Frohlich contributed to this report.