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An international contact group is due to hold talks on Libya's future in Doha on Wednesday.
Koussa sought refuge in Britain on March 30 after quitting the government of Libyan leader Muammar Qaddafi and was later questioned by Scottish police over the 1988 Lockerbie bombing, but the British government said he was now free to travel.
"We understand he is travelling today to Doha to meet with the Qatar government and a range of Libyan representatives to offer insight in advance of the contact group meeting," a Foreign Office spokesman said.