Izzat al-Rishq, a member of the group's politburo, said on Sunday that Hamas wanted the deal to include the release of 1,000 named Palestinian prisoners in exchange for an Israeli soldier captured in a raid near Gaza in June involving the Hamas' military wing.
Al-Rishq said: "This visit is intended to maintain contacts with the brothers in Egypt, who are doing their best to mediate a deal and talk with the Israeli side. The elderly, women and children must be set free also."
An Egyptian official had said earlier on Sunday that Mishaal would be part of the Hamas delegation.
The official, who asked not to be named, said Omar Suleiman, Egypt's intelligence chief, had presented Mishaal with the latest version for a prisoners' exchange deal earlier this month during his visit to Damascus, where Mishaal lives.
Asked what was new in the latest Egyptian proposal, the official said: "It's only about the number of [Palestinian] prisoners being released."
Soon after the capture of Gilad Shalit, an Israeli corporal, on June 25, Egypt tried to arrange an exchange with Hamas, insisting that there could be no time lag between the release of the soldier and that of the Palestinians.
Al-Rishq said Hamas was now willing to show flexibility on the timing of any proposed exchange.
He said: "We still don't trust the Israelis. A number of the Palestinian prisoners must be released simultaneously with the Israeli soldier. We could accept an arrangement whereby the rest would be freed later."
One of three Palestinian groups holding the Israeli soldier in the Gaza Strip said on Saturday it expected a solution to the crisis within days based on the Egyptian proposal, though it said any deal still depended on Israel.
Al-Rishq said the Hamas delegation would discuss with Egyptian officials efforts to form a new Palestinian government that would include Hamas and President Mahmoud Abbas's Fatah faction.
Talks on a coalition government collapsed because the two rivals could not agree on terms that might have led to an easing of Western sanctions, designed to push Hamas to recognise Israel, renounce the armed struggle and accept past accords.
Hamas says the Palestinians would not gain anything by compromising without similar moves from Israel.
Javier Solana, the European Union foreign policy chief, said on Sunday he hoped for news on a government of Palestinian technocrats within days.