The sources said there was a consensus on a long-term ceasefire in the besieged enclave, yet some sticking points remained, including Hamas arms.
Hamas repeatedly said it was not willing to lay down its arms, a key demand for Israel.
Earlier, Egyptian state-affiliated Al Qahera News TV reported Egyptian intelligence chief General Hassan Mahmoud Rashad is set to meet an Israeli delegation headed by strategic affairs minister Ron Dermer on Monday in Cairo.
The sources said the ongoing talks included Egyptian and Israeli delegations.
There was no immediate comment from Israel and Hamas. Mediators Egypt and Qatar did not report developments on the latest talks.
Qatar's Prime Minister Sheikh Mohammed bin Abdulrahman Al Thani said on Sunday that a recent meeting in Doha in efforts to reach a ceasefire made some progress, but noted there was no agreement on how to end the war yet.
He said the militant group was willing to return all remaining Israeli hostages if Israel ended the war in Gaza.
But Israel wants Hamas to release the remaining hostages without offering a clear vision on ending the war, he added.
Israel resumed its offensive in Gaza on March 18 after a January ceasefire collapsed, saying it would keep up pressure on Hamas until it frees the remaining hostages still held in the enclave. Up to 24 of them are believed to still be alive.
The Gaza war started after Hamas' October 7, 2023 attack which killed 1200 people and saw 251 hostages taken to Gaza, according to Israeli tallies.
Since then, Israel's offensive on the enclave killed more than 52,000 people according to local Palestinian health officials.
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