* Alliance members bridling at length of bombing campaign
* Gaddafi emissaries say he is ready to quit: France
* U.S. casts doubt on French assertion
* Rebel official predicts Gaddafi departure by end-August (Updates with U.S. comment, French vote)
TRIPOLI July 12 (Reuters) - Emissaries from Libya's Muammar Gaddafi have been in contact with NATO members to say he is ready to leave power, France said on Tuesday, the latest sign of a possible negotiated end to the crisis.
"A political solution is more than ever indispensable and is beginning to take shape," French Prime Minister Francois Fillon said in Paris.
NATO powers have until now been focused firmly on airstrikes and backing the rebels trying to overthrow Gaddafi. But five months into the insurrection and with no sign of a breakthrough, attention is switching to a political solution.
Earlier, French Foreign Minister Alain Juppe had said emissaries from Gaddafi's government were in contact with several NATO members, though there were no fully-fledged negotiations yet.
"Emissaries are telling us Gaddafi is ready to go, let's talk about it," Juppe said. "The question is no longer about whether Gaddafi goes but when and how."
"Everybody is in contact with everybody. The Libyan regime is sending messengers everywhere, to Turkey, New York, Paris," Juppe said on France Info state radio. "There are contacts but it's not a negotiation proper at this stage."
How reliable the information from the emissaries is remains unclear. Many observers urge caution about taking everything emanating from the Libyan government at face value because previous peace offers have come to nothing.
Washington expressed doubts about such contacts, saying messages received were contradictory and unclear.
State Department spokeswoman Victoria Nuland said the United States was aware that "a lot of folks" claiming to speak for Gaddafi were in touch with various western countries.
But the "messages are contradictory" and there is no clear communication that "Gaddafi is prepared to understand that its time for him to go," she said.
Sources say the envoys are close aides to Gaddafi who are in contact with intermediaries who report directly to President Nicolas Sarkozy.
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It was not obvious how Gaddafi, who has refused to even contemplate relinquishing power, could be persuaded to change his mind through negotiations.
NO OTHER OPTIONS
Some analysts say Gaddafi will step down only if he is left with no other options, but appeals for negotiations could be regarded in Tripoli as a sign the West's resolve is weakening, and encourage Gaddafi to hold on longer.
Karim Bitar, a Middle East expert at Paris-based think tank IRIS, said negotiations between the rebels and the Gaddafi camp were likely to be extremely complicated.
"It's not a country where power is easily shared. There are 6 million people, a few powerful tribes and oil reserves almost all in just one area, so it won't be easy to find a sort of an agreement where Gaddafi is on the sidelines and cedes power."
In an interview with French daily Le Figaro on Tuesday the Libyan Prime Minister Baghdadi al-Mahmoudi said Tripoli was ready to "negotiate without conditions" but the bombing must stop first. "You don't create democracy under bombs," he said.
Asked if Gaddafi could be excluded from a political solution, Mahmoudi suggested he could stand aside. "(He) will not intervene in discussions," he said. "He is ready to respect the decision of the people."
France spearheaded the West's military intervention in Libya but is growing impatient. Sarkozy took a gamble by taking a personal role in supporting the rebels, but is now anxious to avoid costly military operations running into the start of campaigning for the April 2012 presidential election.
French lawmakers in the National Assembly voted overwhelmingly to extend funding for the military campaign.
Western officials talking about a possible deal are making references to a plan drawn up by the African Union. That plan allows for a ceasefire, access for humanitarian aid and the launch of a dialogue about Libya's future.
After a summit earlier this month, African Union leaders said Gaddafi's administration had agreed he would not take part in the negotiating process, but it was not clear if that also meant there would be no future role for him.
Italian Foreign Minister Franco Frattini, visiting Libya's neighbour Algeria on Tuesday, joined calls for a negotiated deal. "We stress the need for a ceasefire and dialogue in Libya with the exclusion of Gaddafi and his family, who must leave power," Frattini told a news conference.
Frattini said the chaos inside Libya was being exploited by Islamist extremists based in the Sahara desert to acquire weapons, the first senior Western official to acknowledge that publicly.
Thousands of Libyans, inspired by revolutions in neighbouring Egypt and Tunisia, rose up against Gaddafi's rule in February. That prompted a crackdown by his security forces in which, rights groups say, thousands of people were killed.
The Western bombing campaign began a month later under a United Nations mandate to protect civilians.
Ali Tarhouni, the oil chief with the rebel National Transitional Council, travelled from the council's base in the eastern city of Benghazi on Tuesday to the Western Mountains, an area south of Tripoli also held by the rebels.
He said he expected a military breakthrough by the rebels in the west with Gaddafi forced out "by the end of Ramadan".
The Muslim holy month begins at the start of August. (Additional reporting by Hamid Ould Ahmed in Algiers, Peter Graff in Zintan, Nick Carey in Misrata, and Brian Love, John Irish, Alexandria Sage and Vicky Buffery in Paris; Writing by Christian Lowe and Giles Elgood; Editing by Robert Woodward)