Other conditions set by Hamas include that the Palestinian role should be determined by an agreement between Hamas and the Palestinian Authority (PA).
The movement also said it was against Israel's veto power to close the crossing.
Hamas further proposed that the entry into and out of Gaza through Rafah should not only be confined to Palestinians carrying identification cards issued by the PA.
Thursday's deliberations come a day after Mahmoud Abbas, the Palestinian president, met Hosni Mubarak, Egypt's president, and asserted his refusal to deal with Hamas.
Meshaal is expected to meet Ahmed Abulgheit, Egypt's foreign minister, and Omar Sullieman, its head of intelligence.
In related news on Thursday, Israeli soldiers killed a Palestinian man in the southern Gaza Strip, local medics and the Israeli military said.
Twenty-year-old Mahmud al-Daalsah, a member of the Al-Aqsa Martyrs Brigades, was killed in an exchange of fire with Israeli soldiers near the town of Rafah, medics and witnesses said.
An Israeli military spokesman said "the combatant was killed when he approached the security barrier" between the territory and Israel.
Since Israel and the Palestinians revived their peace negotiations in late November after a seven-year freeze, at least 145 people, mostly fighters, have been killed by Israeli troops in Hamas-run Gaza.
Thursday's death brings to 6,105 the number of people killed, a vast majority of them Palestinians, since the start of the second Palestinian uprising in September 2000, according to an AFP tally.