Libyan officials are being reported as saying that the Arab League's inefficiency in dealing with the crises over Iraq and the Palestinians is behind their desire to leave.
Libyan leader Muammar Gaddafi has made no secret of his disappointment in his fellow Arabs, and has threatened to pull out of the 22 member body before.
In March this year he threatened to pull out in a row over a Saudi Mid-East peace initiative.
On that occasion Mr Moussa flew to Tripoli and the idea was put on hold.
'Cowards'
During the 1990s the Libyan leader was very bitter about the Arab League's refusal to break United Nations sanctions, now suspended, that were imposed on Libya in connection with the Lockerbie bombing.
As a result, Libya turned its face towards its southern neighbours, building closer ties with African nations.
In September, Colonel Gaddafi was reported to have raised the issue of leaving the Arab League again in protest at "official Arab cowardice" in confronting Israel and the United States.
He said he was ashamed to be Arab.
Mr Musa, who is admired in Libya for his strong stance on Israel, went to Tripoli again to try to calm Colonel Gaddafi's anger.
Since its creation 60 years ago, the Arab League's effectiveness as a regional organisation has been severely hampered by divisions between its member states. The BBC's reporter in Cairo, Hebeh Saleh, says that if the colonel feels he has made his point, he may yet allow himself to be persuaded by Amr Moussa.
That appears to be what other Arabs are banking on.
Egyptian Foreign Minister Ahmed Maher said Libya's views would be taken into consideration by other Arabs and the rift would be healed.