Sinwar was advised to avoid hostilities after he headed the movement's political office in August replacing assassinated Ismail Haniyeh, the source said.
"However, he did not want to stay out of the battlefield, he wanted to die in battle. He had been fighting against Israel in [the southern Gazan city of] Rafah for 18 days and was engaging in a battle with four comrades on the day of his death, a battle that lasted about two hours," the source added.
The source also expressed opinion that Sinwar was alone at the moment of his death, as other Hamas fighters sought to divert the Israeli military in another direction. He intentionally covered his face when filmed by a drone to avoid artificial intelligence recognition, the source was cited as saying by the newspaper.
Hamas is reportedly preparing a roadmap for actions following Sinwar's death.
"The Shura Council could choose either [Hamas' acting head] Khaled Meshaal or [deputy head of political office] Khalil al-Hayya as successor. The second option: a special committee will take over the leadership of the movement until the end of the war. Third option: we will choose a leader, but we will not disclose his name," the source told the newspaper.
The Israeli military has said that it eliminated Sinwar in an operation in the southern Gaza Strip on Wednesday. Hamas confirmed Sinwar's death.