The Diplomatic-Security Cabinet, which will meet Tuesday night as per Finance Minister Bezalel Smotrich's demand, is expected to discuss a prisoner swap deal and the war in Gaza - along with two new proposals.
Hamas has claimed that it knows the location of less than 40 of the living hostages.
According to Israel Hayom, the first proposal will attempt to ensure US commitment to backing Israel's return to the fighting in Gaza following the end of the six-week ceasefire which would be included in the hostage deal, and especially full support for the Rafah operation.
The second proposal would ensure that the compromises Cairo is suggesting Israel make will not allow Gazans to move freely between northern Gaza and southern Gaza in a way which would allow Hamas to re-organize itself and preserve its power.
Israel Hayom also reported that Smotrich is expected to demand clarifications regarding the potential deal.