Melissa Reid, from Lenzie, was arrested last August after being caught in possession of £1.5 million worth of cocaine at Lima International Airport.
Both she and accomplice Michaella McCollum Connolly initially claimed they were kidnapped while on a working holiday in Spain.
The pair claimed they were then forced to travel to Peru to smuggle 11kg of the class-A drug out of the country.
After a trial in December, they were sentenced to eight years in prison. Both had their terms reduced to six years and eight months after entering guilty pleas. They share a cell in the Virgen de Fatima prison, known for overcrowding and disease.
However, last month Reid submitted a prisoner transfer request with her family paying a civil fee of around £3500. The Peruvian Government has written to Scottish authorities to finalise the move, with the justice minister paving the way for her arrival.
Reid's father told a Sunday newspaper he met Justice Secretary Kenny MacAskill who said he would not oppose a transfer.
Mr Reid said: "We understand the Scottish Government can't promise to magic her back home and they won't pull any strings, but it was very comforting to hear they are not against any move. He told me, 'she is one of us' and explained that, if and when Peru agrees a transfer, they would not block it."
If returned to Scotland, Reid is likely to be classified as a low-risk prisoner who could later apply for home leave or even early release under electronic tagging. She would also have access to rehabilitation processes and medical care.
Mr Reid added: "The prospect of my daughter spending nearly seven years in the Peruvian prison system, thousands of miles away, scares me. I already have real concerns about her health and well being and worry she could suffer permanent problems as a result of being there long-term.
"If she was back home in Scotland, she could serve her time in conditions that would not breach her basic human rights."
If the prisoner transfer is approved on both sides, it is thought that Reid could be in Scotland within two months — in time for her 21st birthday in August.
She would then be received as a new arrival, meaning she would be eligible for release after completing half of her sentence.
In a letter to her parents, Reid said: "Although I won't exactly be going right home and will be going to a prison, at least I will get to speak my own language 24/7 and be around people similar to me.
"I am so surprised my request is being dealt with so quickly and urgently and although I know it has not yet been accepted, I feel confident about the process now after having some news so quickly.
"Who knows, I could be out of this place before my 21st birthday and that would really be a dream."
A spokesman for the Scottish Government confirmed Mr Reid had met Mr MacAskill who was in contact with the UK Foreign Office.