Lawyers for the Libyan ex-agent, jailed for at least 27 years for the 1988 plane explosion over the Scottish village of Lockerbie, made the application two days ago to the High Court in Edinburgh, said legal firm Taylor and Kelly.
It still has to be approved by the court and a hearing will take place there Tuesday, the Scottish Courts Service said.
Libya has also applied for him to be transferred to serve his sentence in a prison in his homeland and dropping the appeal could pave the way for this to take place.
"There cannot be an application under the prisoner transfer agreement where there are ongoing (legal) procedures," a Scottish government spokeswoman said, adding that an ongoing appeal had "no bearing" on his application for compassionate release.
British media reported earlier this week that Megrahi could be set free on compassionate grounds next week as he has prostate cancer which his supporters say is terminal. Officials say no decision has yet been taken.
There are three possible avenues by which Megrahi could be sent home.
The first would be a successful appeal against conviction. His second appeal against conviction got under way in a Scottish court in April after a first attempt failed in 2002.
The second would be release on compassionate grounds which reports suggest Scottish Justice Secretary Kenny MacAskill could approve next week in time for Megrahi to return to Libya before the start of Ramadan, the Muslim holy month.
The third would be for him to be transferred back to Libya to serve out the rest of his jail term following a prisoner transfer agreement signed between Britain and Libya earlier this year.
The plan to drop the appeal prompted claims from some Scottish lawmakers that Megrahi had been pressured by officials but First Minister Alex Salmond denied this.
"We have no interest in pressurising people to drop appeals, why on earth should we?" he said. "What Mr Megrahi does with his appeal is a matter for him and his advisers, not for the Scottish government."
The move has, though, dismayed those who believe Megrahi, 57, was wrongly convicted over Britain's worst ever terror attack and that there are more facts which need to emerge in the case.
Professor Robert Black, a leading Scottish academic lawyer who helped set up the legal framework for Megrahi's trial in The Netherlands, told Scottish newspaper The Herald: "I just don't understand why he is dropping the appeal now.
"If the appeal is to be dropped then the next step is to press for a public inquiry ... once the appeal is dropped this is really the only avenue available for people to get questions and issues into the public domain."
Relatives of those who died in the Lockerbie bombing are split on whether Megrahi should be set free.
Susan Cohen, whose daughter was killed in the bombing, has said Megrahi's release would be "a disgrace."
"This man is a mass murderer," she told Sky News television this week from the US. "I'm sick of hearing about compassion and sympathy. If the man is ill, he can get treatment in prison. If we send him back, he'll be a hero."
Briton Jim Swire, whose daughter Flora died, said it was "inhumane" to keep Megrahi in prison and it would be "to Scotland's credit" if he was sent home.
The United States has expressed its opposition to any early release, saying Megrahi should spend the rest of his time in jail, and a delegation of US senators conveyed this message directly to Libya during a brief visit Friday.
Relations between Britain and Libya have warmed in recent years after Tripoli's renunciation of weapons of mass destruction in 2003 and an agreement to pay compensation to Lockerbie victims' relatives.
Source: AFP Global Edition