"We have three problems - the infected children, the dead children and the convicted Bulgarians. In this case we have to solve the three problems together," Foreign Minister Muhammad Abd al-Rahman Shalgam said on Sunday after talks with his Bulgarian counterpart in the Netherlands.
In May, a court sentenced the five nurses and a Palestinian doctor to death for intentionally starting an epidemic in a Benghazi hospital that infected 426 children and killed at least 40.
The United States and the European Union have denounced the verdicts.
Libya wants the Bulgarian government to talk directly to the families of the victims and agree on financial compensation, Shalgam said.
He added Libya wants the talks to include paying for the construction of a hospital for Aids victims.
"If these two steps are fulfilled, then we can talk about the third step, which is related to reversing the verdict," he said shortly after returning from the Netherlands.
Shalgam said the European Union had to be involved as well.
Many of the nurses have said they confessed under torture, and western medical experts have testified that the epidemic began before the nurses arrived at the hospital, probably due to poor sanitary conditions.