The US tycoon was asked to endorse a statement drafted by the First Minister's chief of staff saying the decision – which provoked fury in the US – would "break the cycle of violence around the world".
He was approached days after Abdelbaset Ali Mohmed al Megrahi was released from jail in Scotland and nine months after the Scottish Government had rubber-stamped Trump's plans for a £1 billion golf development on the Aberdeenshire coast.
Mr Trump, who is now in dispute with the Government over a proposed offshore wind farm within sight of his golf course, said he declined to put his name to the statement.
Labour said the approach suggested the First Minister believed he was owed a favour by the tycoon, although the Government insisted it was "perfectly entitled" to seek support.
The statement was drafted by Geoff Aberdein, then a special adviser and now the First Minister's chief of staff, in the days after Megrahi's release in August 2009.
It followed mounting anger in the US, including criticism by FBI chief Robert Mueller.
The draft statement in Trump's name said: "It must have been a hugely difficult decision for the Scottish Government to make and, of course, for most of our own United States families who lost loved ones, it would always be impossible to accept.
"Their reaction is entirely understandable and, as an American, I personally would sympathise with the US families.
"However, I am certain that the Scots issued this release for good reasons and I would hope that it might break the cycle of violence around the world, and replace it with reciprocal gestures. In any event it won't stop my love affair with Scotland and the Scots. No-one should ever demean that country.
"Too many Scottish soldiers have died in Iraq and Afghanistan for the head of the FBI to lecture Scots on fighting terrorism."
The statement was leaked as the Trump Organisation has been stepping up pressure over a planned offshore wind farm.
The golf course has opened but Mr Trump has reiterated he has shelved plans for a hotel and holiday homes until a decision is made.
He has warned the sight of turbines would put his hopes of attracting the 2022 Ryder Cup in jeopardy, and has also hit out at the RSPB after it withdrew its objections to turbines.
Labour MSP Lewis Macdonald said: "Alex Salmond needs to tell the Scottish people why he thought it was appropriate to use his political and personal relationship with Donald Trump to gain support for such a controversial decision.
"It would appear the First Minister thought Mr Trump had a favour to return, even if the US tycoon didn't agree."
Scottish Conservative deputy leader Jackson Carlaw MSP said: "Alex Salmond needs to explain without delay what on earth the Scottish Government was thinking when it took this action.
"Donald Trump, like most people in Scotland and almost everyone in the US, clearly realised the release of Megrahi was a huge mistake.
"This is another murky development in a sorry saga."
A spokeswoman for the First Minister said the Government was "not disputing" the contents of the leaked email.
However, she said of the controversial decision to release Mr Megrahi: "We were perfectly entitled to hope for support from international stakeholders."
"We understand Mr Trump did not support this decision, which was entirely up to him.
"None of this will have any bearing on the Scottish Government's proper consideration regarding the European Offshore Wind Deployment Centre."