Regional and world leaders are pushing for a truce to end the bloodiest conflict in the besieged territory since 2009, which has killed more than 340 Palestinians and five Israelis in 13 days of Israeli airstrikes and cross-border rocket fire by militants.
Hamas "received an invitation, through mediators, for a delegation headed by (chief-in-exile) Khaled Meshaal to visit Cairo and discuss the Egyptian initiative," it said in a statement.
It said the Islamist movement's "response was that its position on the initiative is known, but it is at the same time ready to cooperate with a move by any party that will achieve the specific Palestinian demands."
Hamas earlier in the week rejected an Egyptian proposal for a truce - which was accepted by Israel - saying that it had not been consulted and demanded a full settlement before it ceased firing.
An Egyptian foreign ministry official said he could not confirm or deny the new invitation.
Hamas relations with Egypt have hit a low since Cairo's military regime took power last July, ousting Hamas ally the Muslim Brotherhood.
Turkey and Qatar, where Meshaal is based, are more sympathetic to the movement.
Hamas spokesman Fawzi Barhum told AFP Saturday the movement had "given the demands of the resistance to all the parties concerned, including Qatar, Turkey and the Arab League and (Palestinian president) Mahmud Abbas."
Abbas was to meet Meshaal in Qatar Sunday to discuss the truce.
Hamas's demands include an end of the "war on the Gaza Strip," a complete lift of the siege on it, opening the Rafah crossing with Egypt, freedom of movement in the border areas, cancelling the buffer zone and expanding the freedom to fish 12 nautical miles from shore.
In addition, Hamas demands the release of its members who had been freed in a 2011 deal and recently re-arrested in an Israeli crackdown on the West Bank.
A senior official in the Palestine Liberation Organisation, which is dominated by Abbas's Fatah party, said in an interview on Palestinian television that the West Bank-based leadership recognised Hamas's demands.
"These are also our demands," Yasser Abed Rabbo said.
"If Gaza is broken, all Palestinians will be broken."