Peruvian chief prosecutor Juan Mendoza Abarca said the 20-year-olds, who face a minimum of six years in jail for bringing cocaine into the country, could be home within weeks if they hand over all details about the group responsible for the £1.5 million smuggling plot.
Although they have pleaded guilty to drug smuggling, Reid, of Lenzie, and McCollum, from Dungannon, Northern Ireland, insist they were forced into smuggling drugs by a gang that kidnapped them from Ibiza where they were working summer jobs.
Juan Mendoza Abarca, chief prosecutor, said: "There is a possibility these two women can be out in around two months and never have to go back. But they have to give us all the information they have, names, addresses, contact details and so on, so we can bring the drugs gang here in Peru and abroad to justice.
"The women's story about being kidnapped and forced to Peru at gunpoint is illogical. Our experience is that drug mules come to Peru from Europe of their own free will to make money."
Meanwhile a former boyfriend of McCollum has claimed her party girl public image was not a true reflection of her character.
Part-time DJ Brad Houston had a five-day fling with her shortly before her arrest. "She's a 20-year-old girl, like anyone's normal daughter. She's not a drug dealer," he said. Houston also believed McCollum was innocent as she had no story to account for her week-long disappearance, which sparked a global appeal.