He said he expected "the whole financial settlement" to be completed soon, adding: "The families will then issue a statement announcing that the settlement is done."
This was part of a deal organised by the Kadhafi Foundation, a charity which has been involved in mediating a resolution to the case.
In return for the money, the relatives will sign a declaration to be handed over to the Supreme Judiciary Council, saying they no longer insist on the death penalty being carried out.
Sergei Stanishev, the Bulgarian prime minister, said: "The fact that Libya's Supreme Judiciary Council session was called in such a short term after the latest court ruling shows the efforts of the Bulgarian government, the European Commission and the EU countries."
But Bulgaria and the EU refuse to accept the idea of compensation, as it might imply the six were guilty, and government officials from Bulgaria have denied that they have sent money to the families.
The EU has, though, offered a fund to pay for the children's future care.
Libyan officials have said the council could take several sessions to reach a final decision and will only agree to the release of the nurses if a settlement has been reached in the private talks between the families and the EU.
Mohammed Abdel-Rahman Shalgam, the Libyan foreign minister, said: "The council will take into consideration several factors like compensation, the age, and the time spent by the prisoners in jail."
The six medical workers deny having infected more than 400 children and say their confessions were extracted under torture.
Experts and outside scientific reports have said the children were contaminated as a result of unhygienic conditions at a hospital in the northeastern coastal city of Benghazi.
Fifty of the infected children died. Libya is under international pressure to free the medical workers.