"His condition has taken a significant turn for the worse in recent weeks," he said.
"He applied to the High Court of Justiciary to abandon his appeal."
The development comes less than two days after reports that the former Libyan agent could be granted an early release from prison by next week.
|Some 259 passengers and 11 people on the ground were killed in the bombing
Alan Fisher, Al Jazeera's correspondent in London, said he had been told that a decision on al-Megrahi was imminent.
But the Scottish government said while it was considering an early release, no decision had yet been made.
Reports of a possible early release have divided families of the bombing victims.
Many British relatives have said they are not convinced by the case against al-Megrahi, and say he should be released.
But US families of some of those killed said he should be left to serve the rest of his life sentence in Scotland, a view also shared by the US state deparment.
Al-Megrahi, who has repeatedly protested his innocence, lost an appeal in 2002 and last year failed to secure his release on the grounds he was dying.
In May this year, his lawyers began an appeal against his conviction at a court in Edinburgh, saying the case against him was flawed.
The court in Edinburgh will meet on Tuesday to consider the request to drop the appeal, a spokeswoman said.
Analysts say politics will influence any decision over al-Megrahi's future as much as legal or medical factors.
Libya has been making progress towards shedding its pariah status and being accepted by the West, and the release would mark an important milestone.
Under a transfer agreement signed between Libya and Britain, al-Megrahi could be sent back to Libya to serve the remainder of his minimum 27-year jail sentence, our correspondent reported.
Libya accepted responsibility in 2005 for the Lockerbie bombing and said it would pay about $2.7bn in compensation to the families of those killed in the attack.
That move prompted the lifting of international sanctions against Libya and led to a restoration in diplomatic ties between Tripoli and the West.