Melissa Reid and her family are waiting for an agreement to be finalised between Peru and the UK so that she can serve out the rest of her sentence in a Scottish jail.
However she and the Northern Irish woman Michaella McCollum who was convicted with her could now apply to be free in November next year, having served just a third of the eight year and six months sentences they received.
A new law specifically designed to cut the number of "small fish" serving time in Peruvian jails for drugs offences will allow foreigners to serve one-third of their sentences before applying for release.
Reid, who recently turned 21 in jail, and McCollum, also 21, were convicted of attempting to smuggle £1.5m worth of cocaine out of Peru after being arrested in August last year.
The director of the Peruvian Prison Service Perez Guadalupe told a Sunday newspaper: "They can apply to be expelled because they have a six years, eight month sentence and they will just have to serve one-third, including time reduction for work and study. This law was created for people who are the last link on a chain, like those girls who are not in a gang or criminal organisations."
Reid's father Billy, from Lenzie, said his daughter was still hoping for a transfer which was applied for in January.
However he said the law change could be something the so-called "Peru Two" could seek to take advantage of, particularly if political or bureaucratic hurdles delayed plans for the women to apply to serve the remainder of their sentences in the UK, under Britain's extradition treaty with the South American country.
Mr Reid said: "Having seen the conditions that she's living in her health is still a major concern. The sooner we get her back home the better. But this is great in that it's another route for her."