A delegation led by General Ahmed Abdel Khalek, Palestinian affairs chief in the Egyptian intelligence service, has shuttled between the two sides in a bid to broker what would be the first such exchange since 2011, the source said, speaking on condition of anonymity.
The delegation held a round of talks in Israel sandwiched between two rounds of talks in Gaza on Thursday and Friday.
“The Egyptian intelligence delegation talked with Hamas and with the occupier and delivered messages,” the source said.
Hamas demanded that Israel restore the freedom of all prisoners who had been arrested since their release under the last swap deal in 2011.
They also requested the release of “children, women and sick people” held by Israel in return for information about Israelis held by Hamas.
Hamas is holding at least two Israeli civilians who slipped across the border illegally in 2014 and 2015.
It also holds the remains of two Israeli soldiers who were killed in 2014 in the most recent of the three wars that have pitted Hamas against Israel since the Islamists seized Gaza in 2007.
“The delegation is currently seeking to finalise a swap deal and we hope that it will be completed as soon as possible,” the Hamas source said.
The last prisoner exchange between the two sides in 2011 centred on Israeli soldier Gilad Shalit, captured by Hamas in 2006, in return for whom Israel released 1,000 Palestinian prisoners.
The latest talks come after Israel and Hamas renewed an Egyptian-brokered truce late last month after more than three weeks of tit-for-tat fire across the border.
Under the deal, Israel has allowed the gas-rich Gulf state of Qatar to funnel tens of millions of dollars of aid into Gaza in return for a halt to rocket and other fire into Israel.