Libya and the UK ratified a prisoner transfer agreement last week
The Libyan authorities have requested that the man convicted of the Lockerbie bombing be transferred from Scotland.
The application for the transfer of Abdelbaset Ali al-Megrahi was received by the Scottish Government.
The move came after a prisoner transfer agreement was ratified by the UK and Libyan governments last week.
Megrahi was convicted in 2001 of carrying out the 1988 atrocity, which claimed 270 lives when Pan-Am flight 103 exploded over the Scottish town.
The Scottish Government, which has the final say on the transfer request, said the application would be considered by officials who would advise ministers.
I am not opposed to this, simply because I don't believe the man is guilty as charged
Dr Jim Swire
Father of Lockerbie victim
Under the terms of the prisoner transfer agreement, it is thought the process could take about 90 days - although it could take longer if further information is required.
Al-Megrahi, who is terminally ill with prostate cancer, is currently being held in Greenock Prison.
The 57-year-old, who has already lost one appeal, has been conducting a second appeal against his conviction. It is being heard by five judges in Edinburgh.
Although the appeal can continue while Scottish ministers consider the application from the Libyan authorities, a transfer would not be possible while criminal proceedings are taking place.
That means it would not be possible for al-Megrahi to return to Libya unless he dropped his appeal.
Dr Jim Swire, whose daughter Flora was on board the Pan Am flight, said it was only right Megrahi should be allowed home.
"I am not opposed to this, simply because I don't believe the man is guilty as charged and I don't think Megrahi should be in prison," he said.
But Barrie Berkley, who lost his son Alistair in what was the worst terrorist attack in UK history, said he hoped the appeal would continue.
"I would rather the appeal be completed first and I hope the courts would facilitate it going through without any further delay," said Mr Berkley, of Hexham, Northumberland.
"We want the appeal to go through because it's the main means of us getting further information about how our family members died or why they died.
"We really want to know whether the Libyans were behind this and Megrahi was behind it."
Scottish First Minister Alex Salmond previously raised concern that his government was not consulted by UK ministers before a memorandum of understanding on prisoner transfer was signed with Libya.
A spokesman for the then prime minister, Tony Blair, insisted at the time that no deal had been signed over the future of Megrahi, who was tried under Scottish law at a specially convened court at Camp Zeist, in the Netherlands.
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