Libyan Abdelbaset al-Megrahi was convicted of the bombing of Pan Am flight 103 over Scotland in which 270 people were killed 25 years ago.
Megrahi, who was released from jail by the Scottish government on compassionate grounds after being diagnosed with prostate cancer, died last year protesting his innocence.
His family hope the Libyan government can help fund the appeal process.
His brother Abdel-Hakim Al-Megrahi told the BBC: "Yes, we want to appeal and we wish for the truth to be revealed and this is not just for our own benefit but also for the benefit of the families of the victims and for public opinion.
"We need to know who committed this horrible crime. But, as you know, we as a family cannot afford to pay for the appeals process.
"God-willing, the Libyan government will do this, but it has to be launched by the family first."
Earlier this week some of the British relatives of Lockerbie victims said they are considering making another appeal against Megrahi's conviction.
Members of the UK Families Flight 103 group will meet lawyers in the new year to discuss whether to apply to the Scottish Criminal Cases Review Commission (SCCRC), according to Dr Jim Swire, whose 23-year-old daughter Flora died in the bombing in December 1988.
''The intention of some members is to meet with lawyers in January and discuss the best options, the best way to get the truth,'' he said.
''It's a disgrace that we have to wait 25 years to get the truth that should be available from our governments.''
A successful application to the SCCRC could start the third appeal into the conviction.
Megrahi lost his first appeal in 2002, one year after he was found guilty of mass murder and jailed for life.
The SCCRC recommended in 2007 that Megrahi should be granted a second appeal against his conviction.
He dropped his appeal two days before being released from prison in August 2009 on compassionate grounds.
The planned appeals come as claims were made that a Syrian-based Palestinian group was responsible for the bombing.