Abbas and the Jordanian and Egyptian leaders wull also affirm their opposition to any displacement of Palestinians from their lands.
The source described the negotiations as intensive and said a breakthrough could be possible within days.
Solidarity across borders: Egyptian society mobilizes for Gazan aid.
The flight is suspected to have been part of ongoing efforts outside the public view to negotiate for the release of Israeli hostages currently held captive by Hamas in the Gaza Strip.
The PMO stressed that it could not provide assistance to the Palestinians as long as Hamas was holding over 200 people hostage.
Blinken visits Cairo, Saudi Arabia and will land back in Ben Gurion
Egypt has long restricted the flow of Gazans on to its territory, even during the fiercest conflicts.
One of the security sources said Egypt rejected the idea of safe corridors for civilians to protect "the right of Palestinians to hold on to their cause and their land".
The smuggling operation involved transferring the goods from Gaza to the West Bank, followed by swapping trucks that have Israeli license plates for partial entry into Israel.
Aside from a Koran and a firearm, the terrorist was found to be carrying a knife and six magazines.
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