Relatives of the children and the woman claim that they have taken part of Hamas' information, which was announced on Tuesday, but say that they are still waiting for an official confirmation.
At the same time, the office of Israel's Prime Minister Benjamin Netanyahu urges the public not to spread "rumors" after Hamas claimed that the three family members were killed in an Israeli air strike at the beginning of the war.
Nine months old
The father in the family was also kidnapped by Hamas, but was released at the end of January.
One of the sons was only nine months old and the youngest who was taken as a hostage during Hamas' large-scale attack on Israel on October 7, 2023.
On Tuesday, it was also announced that six people who have been held as hostages in Gaza will be released on Saturday, according to Khalil al-Hayya, leader of Hamas in Gaza.
The six people are the last living hostages to be released during the first phase of the ceasefire, according to Khalil al-Hayya. Previously, it was believed that three people would be released on Saturday.
Second phase not finalized
According to the agreement on the first phase of the ceasefire, which lasts for six weeks from January 19, a total of 33 people who have been held as hostages in Gaza will be released during the period.
The releases are being made in exchange for hundreds of Palestinian prisoners being held by Israel.
When phase one is over, another 60 Israeli hostages will still be held by Hamas. The idea is that they will be released in a new phase of the ceasefire, but the conditions for that phase have not been negotiated.