Libya's Supreme Court is hearing an appeal by six foreign health workers facing death sentences for "knowingly" infecting children with the HIV virus.
President Parvanov said he hoped for a breakthrough for the nurses
The five Bulgarian nurses and a Palestinian doctor were convicted in 2004 but say they were made scapegoats for poor hospital hygiene back in 1999.
Bulgaria's president said he believed a breakthrough might soon be reached.
Libya and Bulgaria on Friday agreed to set up a fund for the families of the 426 HIV-infected Libyan children.
Tripoli has previously hinted the verdicts of death by firing squad could be quashed in return for humanitarian aid.
The medics are basing their appeal on the testimony of Western medical experts who have said the outbreak started before they arrived and was probably caused by unhygienic practices.
They say they were initially tortured into making false confessions.
In a newspaper interview, Bulgaria's President Georgi Parvanov said he had reasons to expect a breakthrough in the talks for the nurses' release.
Their freedom would come "at a very high price", he told the daily paper 24 Hours.
A Bulgarian foreign ministry spokesman told the Reuters news agency a verdict could be reached by the end of the year.
He said his view was based on the opinion of the defence team.
But a Libyan official, Sayyed Khaddaf Eddam, said only that there were "indications of a possibility of concluding this matter in a positive way".
The fund for the children's families was agreed during talks in Tripoli earlier this week.
The European Commission, the US and the UK have also signed up to the fund, the Bulgarian statement said.
About 50 of the children infected at the hospital in the Libyan city of Benghazi have died.