Optimism has been expressed in the United States that Libya will soon issue a statement admitting its complicity in the 1988 Lockerbie bombing.
The bombing killed 270 people
Assistant Secretary of State William Burns told American relatives of victims that no deal had yet been reached.
However, he also informed them that progress had been made during talks in London between Britain, the United States and Libya.
The bombing of Pan Am Flight 103 killed all 259 on the plane and 11 people in the Scottish town of Lockerbie.
Abdelbaset ali Mohmed Al Megrahi was convicted of the bombing and jailed for life in January 2001, with a recommendation that he serve at least 20 years.
The Libyan Government has always denied any involvement in the bombing, but leader Colonel Muammar Gaddafi is keen to re-enter the international fold.
I left that meeting with the distinct, definite feeling that an agreement has been reached
Libya is expected to send a letter to the United Nations admitting some responsibility, while also denouncing terrorism.
This should then lead to UN sanctions being lifted, clearing the way for a £2.7bn (£1.68bn) compensation scheme under which families of each victim would receive $10m (£6.2m).
Daniel Cohen, who lost his daughter Theodora in the bombing, was among those who met Mr Burns in Washington on Wednesday.
He told BBC Radio Scotland: "I left that meeting with the distinct, definite feeling that an agreement has been reached.
"The exact form and written copy of the statement of responsibility has not yet been presented to the US or to the British Government, but that is the only hold-up in this.
"He [William Burns] indicated that unless the Gaddafi government does something that is completely untoward that this should be in the hands of the UN Security Council within a couple of weeks."
He said relatives were told that the UN sanctions, which have already been suspended, would be formally lifted if this statement was accepted.
However, the compensation deal for the families would be linked to a lifting of unilateral US sanctions against Libya.
Mr Cohen said he hated the idea of Libya being "rehabilitated".
Megrahi was jailed for life for the atrocity
He said he was prepared to accept the $4m in compensation from Libya which formed part of the original 1991 UN resolution.
A further $6m would be offered to relatives of the victims in two stages relating to the lifting of US sanctions.
"My wife and I have already informed our lawyer that we have an agreement that we will take none of that money because we do not want these sanctions lifted and we feel like hypocrites," he added.
It has always been made clear on both sides of the Atlantic that a "no fault" compensation package from Libya would not be acceptable.