Israel has approached Egypt with a request to mediate in a possible prisoner swap with Hamas, i24NEWS reported on Saturday, citing Al Arabiya.
According to the report, Cairo mediated in recent talks between Hamas and Israel and urged Israel to allow concessions.
Hamas, for its part, has sought the release of a number of Palestinian Arab prisoners held in Israeli prisons.
It also demanded an easing of fishing restrictions on Gaza and a seaport established there.
Hamas has been holding the bodies of IDF soldiers Hadar Goldin and Oron Shaul since the 2014 Operation Protective Edge.
In addition, two Israeli civilians who went missing in Gaza - Avera Mengistu and Hisham al-Sayed - are believed to be held by Hamas as well.
In December, it was reported that Israel had proposed to transfer coronavirus vaccines to the Gaza Strip in exchange for the return of the missing Israelis. Hamas swiftly rejected that offer.
Israel this week transferred 1,000 coronavirus vaccines from the Palestinian Authority (PA) to Gaza without receiving any information on the missing Israelis.