Israel says it is hopeful the ceasefire could be extended again, and Hamas has indicated it is open to that.
Intelligence chiefs from Israel, the US and Egypt have been holding talks in Qatar to discuss a possible new deal.
This could include the release of the first men or military personnel, abducted during the murderous attack by Hamas more than 50 days ago.
Around 160 people remain in captivity.
The office of Prime Minister Benjamin Netanyahu said it had received a list with the names of those to be freed later today as their families are being notified.
For every Israeli citizen returned, three Palestinians will be released from Israeli jails.
