The Libyan Government appears close to admitting responsibility for the 1988 bombing of Pan Am flight 103 over Lockerbie according to the Washington Post.
For years, Gaddafi insisted Libya played no part in the bombing
It would also deposit $2.7bn into an account as compensation for relatives, in line with an earlier agreement.
The paper, quoting sources said to be familiar with the negotiations, said that there could be a signing next week setting up an escrow or holding account at the Bank of International Settlements in Switzerland.
Libya is due to make a formal statement to the UN Security Council on 14 August, the report says.
However, the extent of any admission is unclear. For example, it is unlikely, officials are quoted as saying, that Colonel Muammar Gaddafi would take personal responsibility.
The Libyan Government might instead say that as the employer of Abdelbaset ali Mohmed al-Megrahi, the Libyan agent convicted of terrorism by a Scottish court, it bore responsibility for his actions.
In return, the UN would lift sanctions against Libya and the United States would then start a dialogue with Tripoli about removing its own bilateral sanctions.
However, this would depend on Libya's attitude towards "weapons of mass destruction and support for militant regimes" said an unnamed US official quoted by the Post.
In London, a Foreign Office spokesman said that he could not comment on negotiations between lawyers for the relatives and Libya.
However, the spokesman appeared cautiously optimistic and said that there were "likely to be meetings in the next couple of weeks, though certain things have to happen first".
Last year Libya agreed to pay $10m to the families of each of the 270 victims of the bombing but tied this to the lifting of sanctions.