Three sources, who have knowledge of the matter but spoke on condition of anonymity, told Reuters no agreement had been reached but talks between South Sudan and Israel were ongoing.
The plan, if carried further, would envisage people moving from an enclave shattered by almost two years of war with Israel to a nation in the heart of Africa riven by years of political and ethnically-driven violence.
Israeli Prime Minister Benjamin Netanyahu's office and Israel's foreign ministry did not immediately respond to a request for comment on the information from the three sources.
A spokesperson for the US State Department said, "we do not speak to private diplomatic conversations," when asked about the plan and if the United States supported the idea.
Netanyahu said this month he intends to extend military control in Gaza, and this week repeated suggestions that Palestinians should leave the territory voluntarily.
Arab and world leaders have rejected the idea of moving Gaza's population to any country.
Palestinians say that would be like another "Nakba" (catastrophe) when hundreds of thousands fled or were forced out during the Arab-Israeli war of 1948.
The three sources said the prospect of resettling Palestinians in South Sudan was raised during meetings between Israeli officials and South Sudanese Foreign Minister Monday Semaya Kumba when he visited the country last month.
Their account appeared to contradict South Sudan's foreign ministry, which on Wednesday dismissed earlier reports on the plan as "baseless".
The ministry was not immediately available to respond to the sources' assertions on Friday.
News of the discussions was first reported by the Associated Press on Tuesday, citing six people with knowledge of the matter.
Wasel Abu Youssef, a member of the Executive Committee of the Palestine Liberation Organisation, said the Palestinian leadership and people "reject any plan or idea to displace any of our people to South Sudan or to any other place".
His statement echoed a statement from the office of Palestinian President Mahmoud Abbas on Thursday.
Hamas, which is fighting Israel in Gaza, did not immediately respond to requests for comment.
Israeli Deputy Foreign Minister Sharren Haskel, who visited the South Sudanese capital Juba this week, told reporters that those discussions had not focused on relocation.
"This is not what the discussions were about," she said when asked if any such plan had been discussed.
"The discussions were about foreign policy, about multilateral organisations, about the humanitarian crisis, the real humanitarian crisis happening in South Sudan, and about the war," she said, referring to her talks with Juba officials.
Netanyahu, who met Kumba last month, has said Israel is in touch with a few countries to find a destination for Palestinians who want to leave Gaza.
He has consistently declined to provide further details.
