The source said the meeting had been put off owing to the effect on the families of the Libyan supreme court's decision on Sunday to overturn the death sentences of five Bulgarian nurses and a Palestinian doctor.
The discussions are aimed at finding a deal on compensation for the victims and stoked hopes in Bulgaria that the nurses could one day be freed. Bulgaria said last week it was creating a fund for AIDS-infected children in Libya.
"The discussions that were to have taken place between the families and a Bulgarian association on December 28 were delayed to the adverse effect of the supreme court's judgement on these families," the source told AFP.
"This decision has delayed an agreement between the parties and forced them to adjourn the discussions to a date that will be fixed later," added the source, speaking on condition of anonymity.
The source said that discussions about the payments had been taking place in the presence of international representatives including from the European Union, Britain and the United States.
As well as seeking an agreement on compensation, the talks were looking at finding a way to care for the infected children and set up a centre for them in their town of Benghazi.
The nurses stand accused of transfusing HIV-contaminated blood into 426 children at a Benghazi hospital on Libya's Mediterranean coast. Around 50 of them have since died of AIDS.
The retrial is due to be held in one month in Benghazi. The supreme court's decision had been greeted with dismay by the families.
The Benghazi court that first condemned the medics rejected testimony from foreign experts that the epidemic was due to a lack of hygiene and based its verdict on a report by Libyan experts that blamed the foreign health workers.