"History is in the making. A deal could be announced at any moment," the source said after US Assistant Secretary of State William Burns met Libyan and British officials in London.
Conditions
Under the arrangement, Libya would compensate families of the 259 mostly-American passengers and crew killed in the mid-air explosion of the Pan Am flight over the Scottish town.
Families of the 11 people killed on the ground would also be compensated.
Tripoli would pay up only if a series of steps to remove United Nations and United States sanctions against it, the source said.
That would make the total value of the settlement roughly $2.7bn if all conditions were met.
A Libyan intelligence agent, Abdel Basset al-Megrahi, was convicted of the crime by a Scottish court sitting in the Netherlands.
The British foreign office described the talks as a "useful session".
"We made further progress. Now the delegations are reporting back to the capitals to consult on the next stage," a spokesperson said.
Repeal of sanctions
The comments were mirrored in Washington by the US state department, although officials on both sides of the Atlantic declined to give details.
Family members of passengers killed on Pan Am flight 103 said the state department had invited Lockerbie victims' families to a meeting on Wednesday for an update on the issue.
The source said Tripoli would initially pay $4m per victim into an escrow account once UN sanctions against Libya, suspended after the Lockerbie trial, were formally lifted.
Another $4m would follow if the US removed its national sanctions against Libya, which remain in force.
A final $2m would be paid if Washington also repealed its Iran-Libya Sanctions Act.
If the US failed to lift those measures within eight months, Libya would pay only $1m extra into the account, limiting its total payment to $5m per victim.