The 20-year-old may return home in the coming months after it emerged the Scottish Prison Service is considering a repatriation application from Lima authorities.
Reid pleaded guilty to drug smuggling along with Michaella McCollum from Co Tyrone in September. Both were jailed for six years and eight months.
The pair were working on the Spanish party island of Ibiza last summer when they claim they were forced to board a flight with 24lb of cocaine in food packets hidden inside their luggage.
They were caught with the £1.5 million haul at Lima airport on August 6.
Reid's father said he has met with Scotland's justice secretary Kenny MacAskill and is hopeful that his daughter will serve the rest of her sentence closer to home.
It is understood that in most cases prisoner transfer applications are approved.
Billy Reid, 54, said: "I had a very positive meeting with Kenny MacAskill and he reassured me that Scotland has no issue (with) accepting Melissa back to serve her sentence here.
"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 that they are not against any move."
A Scottish Prison Service spokesman said: "We can confirm that we have received an application from Peru for the transfer of a prisoner."
A Scottish Government spokesman said: "The Justice Secretary had a private meeting with Mr Reid.
"Prisoner transfers are a matter for the Scottish Prison Service.
"The Foreign and Commonwealth Office has responsibility for UK citizens imprisoned abroad. We have been in touch with them regarding Melissa Reid and have asked to be kept informed of developments."