US President-elect Donald Trump said on Monday he had a "very good" phone call with Israeli Prime Minister Benjamin Netanyahu about the war in Gaza, as Israeli statements renewed about progress in the prisoner swap negotiations, indicating the possibility of reaching a deal before Trump's inauguration.

Trump described his conversation with Netanyahu as a "brief phone call," adding, "We had a very good conversation... We discussed what's going to happen."

The US president-elect said he was "trying hard" to help "recover the hostages and stop the war in Gaza."

Meanwhile, the Israeli Broadcasting Authority said that an Israeli delegation had headed to Qatar as negotiations on the deal progressed, but it explained that "the mandate granted to it is limited."

On the other hand, Israeli Channel 12 quoted informed sources as saying that Netanyahu informed Trump of the need to reach a formula in several stages to conclude a prisoner exchange deal with the Islamic Resistance Movement (Hamas).

The sources said that Israel must make "difficult decisions" in order to reach a deal, noting that there are "gaps in the negotiations regarding the number of (Israeli) kidnapped soldiers, Palestinian prisoners and the deployment of the army (in Gaza)."

The sources added that Israeli Defense Minister Yisrael Katz explained that the deal negotiations are focused on the first phase of it.

Channel 12 quoted the Prime Minister's Office as saying, "Netanyahu is making efforts to increase the number of living kidnapped soldiers in any exchange deal."

For his part, the Israeli Prime Minister's spokesman claimed on Monday evening that Hamas is "flexible" regarding the issue of Israeli forces remaining in the Philadelphi Corridor (Salah al-Din Corridor) on the border between the Gaza Strip and Egypt.

The spokesman said that there is progress in the negotiations of the exchange deal, indicating the possibility of reaching a deal before Trump takes office on January 20.

The spokesman said that Trump told Netanyahu during their conversation that he would like to see the war come to an end.

Meanwhile, the Israeli Defense Minister was quoted as saying that the Netzarim and Philadelphi axes will not hinder the conclusion of the deal, and Katz stated that the deal is closer than ever.

Israeli news reports spoke of "unprecedented progress" towards reaching a prisoner exchange deal between Hamas and Israel.

The newspaper "Israel Today" quoted a source described as informed that the indirect negotiations are achieving tangible progress, noting that he had doubted the possibility of reaching a deal just a week ago.

The newspaper reported that the main dilemma is the number of Israeli prisoners who will be released, and that implementing the deal will take a long time.

Meanwhile, the Israeli Prisoners' Families Authority said it had learned that mediators were pressing for a comprehensive deal to stop the war in the Gaza Strip and return the kidnapped soldiers, but Israel was refusing, it said.

The authority added that "the price of the time that passes will be the lives of the kidnapped, and the more time passes, the more their lives are exposed to danger."