Hamas has expressed willingness to agree to an arrangement in which a list of 250 terrorists are released as a precondition to a deal which would see Israel receiving information on the Israelis held in Gaza, Lebanon's Al Akhbar reported.
Earlier this week, Musa Dodin, Hamas's spokesman on prisoners and a member of the political bureau, denied media reports of an increase in negotiations with Israel, saying he did not believe Israel was serious about such a prisoner exchange.
While Israel's prisoners are all terrorists, who actively worked to maim or kill Israelis, those being held by Hamas are both soldiers and civilians.
IDF soldiers Hadar Goldin and Oron Shaul were killed during 2014's Operation Protective Edge, and Hamas has so far refused to return their bodies to Israel for burial, despite requests from the Red Cross to do so.
The other two Israelis, Avera (Avraham) Mengistu and Hisham al-Sayed, are civilians who suffer from mental illness and who crossed into Gaza by mistake.