The Libyan, who died last year, is the only person ever convicted of the bombing of Pan Am flight 103 over Scotland in which 270 people were killed in 1988.
His brother Abdel-Hakim al-Megrahi said the family wanted to discover “the truth” behind the tragedy which took place 25 years ago today.
It came as Prime Minister David Cameron branded the bombing the “deadliest act of terrorism” in UK history.
One of the British victims’ relatives, Jim Swire, whose 23-year-old daughter Flora died in the tragedy, had recently said some of the relatives of the dead were poised to launch an appeal into the conviction in the new year.
First Minister Alex Salmond told MSPs this week that an appeal would be possible, even though Megrahi had died.
He succumbed to terminal cancer at his home in Tripoli in May last year, after being freed from Greenock prison on compassionate grounds in 2009. Megrahi abandoned a second appeal into his conviction in the Scottish courts, but had always protested his innocence.
His brother said he hoped for government assistance to fund an appeal on behalf of the family to clear his relative’s name.
He said: “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. As a family, we want to appeal. We want the Lockerbie files to reopen to know who is responsible.”
Megrahi was found guilty at a specially convened Scottish court in Kamp van Zeist in Holland in 2001, and jailed for life. His co-accused Al-amin Khalifa Fimah was acquitted.
Mr Cameron has paid tribute to the “fortitude and resilience” of those affected by the bombing on the 25th anniversary.
The prime minister said the atrocity remained “one of the worst aviation disasters in history and the deadliest act of terrorism” ever committed in the United Kingdom.
“The loss of Pan Am flight 103 over Lockerbie at 7:03pm UK time on the evening of 21 December 1988 was a shocking event. A loss made more poignant still by being so close to Christmas.
“Though 25 years have passed, memories of the 243 passengers, 16 crew and 11 Lockerbie residents who lost their lives on that terrible night have not dimmed.
“Over the last quarter of a century, much attention has been focused on the perpetrators of the atrocity. Today, our thoughts turn to its victims and to those whose lives have been touched and changed by what happened at Lockerbie that night.
“To families, friends, neighbours, loved ones, and all those caught up in the painful process of recovery, let us say to them: our admiration for you is unconditional. For the fortitude and resilience you have shown. For your determination never to give up. You have shown that terrorist acts cannot crush the human spirit. That is why terrorism will never prevail.”
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 Swire.
He said: “The intention of some members is to meet lawyers in January and discuss the best options, the best way to get the truth. It’s a disgrace that we have to wait 25 years to get the truth that should be available from our governments.”
Scotland’s top law officer Lord Advocate Frank Mulholland announced this week Libya has appointed two prosecutors to work on the investigation into the bombing.