(CNN) -- There is a growing focus among the international coalition on the "end game" in Libya, and whether one option would be to persuade Moammar Gadhafi to step down and go into exile.
But there are mixed signals from the allies about whether that's feasible or desirable.
And there's another obstacle: the ongoing investigation by the International Criminal Court (ICC) at the request of the UN Security Council into alleged "crimes against humanity" by the Libyan leader.
Last week, the chief prosecutor at the court said he was 100% certain that his investigation would lead to charges against Gadhafi and members of his inner circle. Luis Moreno-Ocampo said he was investigating six incidents of violence against civilians in February and was trying to establish who was responsible.
That would complicate any efforts to reach a "negotiated exit" for the Libyan leader. Some of the coalition's most prominent members are hinting that Gadhafi might receive immunity from prosecution in exchange for leaving Libya. Others are ruling that out.
Take the British position. Publicly, Prime Minister David Cameron has said the UK wants to see Gadhafi tried by the ICC.
But on the sidelines of Tuesday's international conference, Foreign Office Minister Alistair Burt told CNN that Britain would not stand in the way of any deal that would allow Gadhafi to go into exile shielded from prosecution. His boss, Foreign Secretary William Hague, put it another way.
"I would like to see him brought to account," he told the BBC, "but of course it is possible for people to go to places where you can't get at them - where the ICC can't get at them."
Hague suggested that Gadhafi taking refuge abroad might be the lesser of two evils - bring about the kind of change that "most of the world and probably most of the Libyan people want to see".
A similar tone was struck by the U.S. ambassador to the United Nations, Susan Rice.
Speaking on ABC Tuesday, she said: "The expectation, both of the Libyan people and the international community is that there needs to be justice for the crimes that are committed. But obviously should there be an opportunity for some sort of arrangement for Gadhafi to step aside that is something the Libyan people will have to judge and we will take it as it comes."
Speaking later Tuesday on the same network, President Barack Obama was asked, If Gadhafi ends up in a villa some place in Zimbabwe with no war crimes trial, is that OK with you?"
The President replied that it wasn't up to him but added: "I think the international community will come together and make a determination as to what the most appropriate way of facilitating him stepping down will be."
It was the Italian Foreign Minister who first floated the idea of Gadhafi going into exile. Franco Frattini said the Italian government was in talks with the African Union and the Arab League about the possibility of granting exile to Gadhafi. He told La Repubblica newspaper that granting exile to Gadhafi might be a way to end the bloodshed, though he insisted no immunity could be offered the Libyan leader.
ICC prosecutor Moreno-Ocampo has been outspoken in his determination to pursue Gadhafi. He said incidents being investigated involved "massive shooting of civilians" by security forces in cities including Benghazi and Tripoli. And Moreno-Ocampo's spokeswoman has said arrest warrants are possible as soon as May.
And the prosecutor has an explicit mandate - from the UN Security Council itself - whose resolution 1970 referred "the gross and systematic violation of human rights" in Libya to the Court and urged all member states to co-operate fully with the ICC's investigation.
Mark Ellis, executive director of the International Bar Association, says that complicates any kind immunity deal with Gadhafi. "Once the prosecutor comes out with an indictment, which he has not so far but he will seek it, all states that are signatories to the ICC would be obligated to turn over Gadhafi to the Hague."
Malcolm Shaw, a senior fellow at Cambridge University's Lauterpacht Centre for International Law, agrees. He told the Guardian newspaper that Resolution 1970 "basically said to Gaddafi, 'You have to fight to the end.' He may have a few short-term options, but the long-term prognosis for him and his family is very difficult."
Plenty of countries don't recognize the ICC's authority, including Sudan, Morroco, Algeria, the United Arab Emirates, Qatar, Iran, Saudi Arabia and India - as well as three permanent members of the UN Security Council: the US, China and Russia. One of them might be an option should the Libyan leader decide t pack his bags. Neighboring Chad -- sometimes spoken of as a destination -- is a signatory to the Rome Statute that set up the ICC.
There is a get-out clause, but it doesn't smell very good. The UN Security Council could pass another resolution. Ellis explains that one article of the statute that governs the ICC allows for an investigation or a prosecution to be deferred for 12 months at a time. That would set the legal stage for a deal for immunity from prosecution for Gadhafi. But Ellis such a manoeuvre would "contradict the concept of justice and accountability. There cannot be any impunity; international law is very consistent on this topic."
All the talk of exile for Gadhafi may well be moot. Publicly, the opposition has insisted he can't be allowed to leave with impunity and must be tried in Libya. More importantly, the Libyan leader doesn't trust the word of western powers. Long before the current conflict he was disenchanted with the detente that he set in motion when he agreed to give up Libya's nuclear and other weapons of mass destruction programs, and negotiated compensation for families of the Lockerbie victims.
In recent years, Gadhafi and other Libyan officials have complained that despite those concessions, the international community has continued to shun his regime while seeking access to Libya's oil.
And the record of Gadhafi's rule suggests defiance rather than surrender, and an almost messianic belief in his own infallibility. "I am paying the price for staying here, and my grandfather who fell a martyr in 1911," he has said. "I will not leave the country and I will die as a martyr at the end."