One that comes to mind for example would be granting Hamas safe passage out of Gaza, to go in exile. (There are precedents such as Duvalier leaving Haiti. Or Arafat's PLO leaving Lebanon, IIRC). Not sure who would accept them and I don't want to hash out the details to push "my" solution, so let's back to the question:
The situation in Gaza hasn't reached yet the point where one could claim that Hamas is about to be eliminated or that they have no choice but to leave. In the previous rounds of fighting (see the timeline since Israeli withdrawal from Gaza) Israel usually aimed at degrading Hamas' capabilities to fire rockets or carry out cross-border attacks, which typically produced a few years of calm. Trying to completely uproot Hamas was perceived as counter-productive, since
- it raised the amount of casualties in the Israeli army
- it increased the risk of Israeli soldiers being taken hostages
- it required a many-months long operation or perhaps reoccupation of Gaza on a permanent basis.
In view of the gravity of 7/10 attacks such a scenario is not excluded anymore, it may still turn out impossible to achieve. Not the lasts role is played by the political and public pressure due to the rising Palestinian casualties.
Another point worth keeping in mind is that Hamas is not the only militant organization in Gaza, but merely the dominant one. Thus, there is no guarantee that eliminating Hamas would eliminate the threat, and that Hamas would not be replaced by something worse.
It is also wroth noting that many members of Hamas leadership do spend their life in exile, out of fear for their lives: e.g. Khaled Mashal, while being a leader of Hamas, spent most of his time in Jordan, Syria and other countries.
Netanyahu declared goals:
I quote here the statement of the goals of operation by the Israeli Prime Minister:
Citizens of Israel, I want to be clear – the war is continuing. The war is continuing. We will continue until we achieve all of our goals: Return all of the hostages, eliminate Hamas and ensure that on the day after Hamas, no element that supports terrorism, educates its children for terrorism, and pays terrorists or their families, will control Gaza. Gaza will no longer constitute a threat to Israel. We will restore security in both the south and the north. We are winning and will continue to fight until absolute victory. We are doing so thanks to the courage of our soldiers and thanks to the self-sacrifice of our sons and daughters, heroes of Israel. I always remember that this victory has a heavy price – our soldiers who gave their lives for us all, our heroes that fell to defend our home.
Von der Leyen proposal
Ursula von der Leyen has recently made a five-point proposal as well:
The five principles for Gaza proposed by von der Leyen are:
- No safe haven for terrorists.
- No Hamas-led government.
- No long-term Israeli security presence.
- No forced displacement of Palestinians.
- No sustained blockade.
Both proposals (Netanyahu's and Leyen's) appear rather unrealistic: ousting Hamas from power might turn out very difficult without significant casualties, and eliminating completely any threat to Israel's security might be possible only after a peace agreement between Israel and Palestinians and creation of Palestinian state, which has failed to realize over three decades of negotiations. The obvious major point of disagreement between the two proposals is the Israeli military presence in Gaza and simultaneous lifting of the blockade.
Al Jazeera
Al Jazeera, citing less high-level sources, claims that it might be impossible to destroy Hamas:
By assenting to the terms of the release, Israel has shown that it can, in fact, negotiate with Hamas, tacitly conceding that it is no closer to eradicating a group that has gone, quite literally, underground. If anything, by laying waste to much of Gaza City and, with it, the institutions of Hamas governance, Israel’s actions have only made the group more elusive.
Hamas-Lite
The difficulty of removing Hamas is that everyone in the Gaza administration owes allegiance to Hamas to some extent. There is also resistance from Iran, which uses the Palestinian cause as a justification for its involvement in the Arab affairs.
Thus, a possible solution is removing the Hamas leadership and depriving it of military capabilities, but leaving the weakened organization to exist and/or subjugating it to the Palestinian Authority. As Foreign Policy describes it:
Despite Israel’s hard-line rhetoric about Hamas, if it succeeds in eliminating Hamas’s military leaders in the short term, a medium-term scenario of Arab-Israeli acceptance of a minor role for a reformed version of Hamas is not far-fetched. Such an iteration of Hamas would be in line with the statement issued following the joint Arab League-Organization of Islamic Cooperation (OIC) summit in Riyadh earlier this month. The statement emphasizes recognizing only the Palestine Liberation Organization (PLO) as the legitimate representative of Palestinians—but also states that all other Palestinian factions should operate “under a PLO-led national partnership.”
At first glance, the national partnership proposed in the Arab League-OIC statement appears more nuanced than the usual power-sharing arrangements among ruling elites that are a common feature of conflict resolution in the region. The proposal is not calling for power sharing between the PLO and Hamas. Rather, the idea is that Hamas—or at least its pragmatic elements—agrees to operate as a subsidiary political actor under the umbrella of the PLO. In theory, this kind of arrangement could mitigate the power abuses and political paralysis that elite bargains have frequently created in places like Lebanon, Iraq, or Libya.
Whether Hamas will go along with this plan is questionable. One of Hamas’s objectives in the Oct. 7 assault on Israel was to highlight the weakness of the PLO and Palestinian Authority, affirming that Hamas is the only true voice of the Palestinian people. Hamas will not want to be seen as having made a huge political compromise.
Deporting low-rank Hamas members
There are apparently discussions between the US and Israeli officials about the expulsion from Gaza of several thousands of low-rank Hamas members - similar to the proposal outlined in the OP.
Israel and US officials have discussed expelling thousands of lower-level Hamas terrorists from the Gaza Strip as a possible option to shorten the war between Israel and Hamas, The Wall Street Journal reported on Thursday.
[...]
The option to expel Hamas terrorists and their families from the Strip aims to provide the terrorists with an exit strategy and make it easier to rebuild Gaza after the war.
The proposal seemingly would not include higher-up Hamas leaders such as Yahya Sinwar or Mohammed Deif. Israeli officials have said that the two, and other Hamas leaders located both in the Gaza Strip and abroad, are "dead men walking."
Update (Jan 4, 2024)
The recent Egyptian ceasefire proposal goes well beyond the "immediate ceasefire" demands, but stops short of eliminating Hamas:
The Egyptian proposal, worked out with the Gulf nation of Qatar, has been presented to Israel, Hamas, the United States and European governments but still appeared preliminary. It falls short of Israel’s professed goal of outright crushing Hamas and would appear not to meet Israel’s insistence on keeping military control over Gaza for an extended period after the war.
[...]
Egypt and Qatar would also work with all Palestinian factions, including Hamas, to agree on the establishment of a government of experts, he said. The government would rule Gaza and the West Bank for a transitional period as Palestinian factions settle their disputes and agree on a roadmap to hold presidential and parliamentary elections, he added.
In the meantime, Israel and Hamas would continue to negotiate a comprehensive “all-for-all” deal, he said. This would include the release of all remaining hostages in return for all Palestinian prisoners in Israel, as well as the Israeli military’s withdrawal from Gaza and the Palestinian militants’ halting of rocket attacks into Israel. Close to 8,000 Palestinians are held by Israel on security-related charges or convictions, according to Palestinian figures.