Melissa Reid, 20, from Lenzie, was stopped along with Michaella McCollum, 20, from Dungannon, Co Tyrone, with 24lb (11kg) of cocaine hidden in food packets in their luggage while trying to board a flight to Spain last month.
Reid and McCollum have claimed they were forced to carry the drugs by an armed gang who threatened them and their family members. Her father, Billy Reid, said that she was negotiating a plea in the hope she would be sentenced to less than seven years in jail, which would allow her to be transferred to the UK to serve her time.
Her mother, Debbie Reid, said: "We still believe she was coerced into it, but we realise she needs to plead guilty, just to get her home basically," Mrs Reid said.
She added: "The conditions in the prison are quite basic, everything has to be paid for from toilet rolls to water so I think she is coming to realise she just wants to get home as quick as possible and this is the route she has to take."
Mr Reid said the plan is to work with the Foreign Office and other agencies to fast-track his daughter's return to Scotland.