Two judges sitting at the High Court in London will give their decision on the appeal by the 32-year-old, who has Asperger syndrome, on Monday.
His father, the Reverend Alexander Love, has warned his son “fears for his life” because he did not think he could cope with the trauma of being sent to America.
Lord Chief Justice Lord Burnett and Mr Justice Ouseley heard arguments during a hearing in November that extradition would not be in the “interests of justice” for a number of reasons, including the “high risk” that Love would kill himself.
Authorities in America have been fighting for Love to face trial on charges of cyber-hacking, which lawyers have said could mean a sentence of up to 99 years in prison if he is found guilty.
Love, who lives with his parents near Newmarket in Suffolk, and also suffers from a depressive illness and severe eczema, is alleged to have stolen huge amounts of data from US agencies, including the Federal Reserve, the US army, the defence department, Nasa and the FBI in a spate of online attacks in 2012 and 2013.
His father told BBC Radio 4′s Today programme: “He is very distressed, he is obviously afraid because he has stated on more than one occasion that he fears for his life because he doesn’t think he can cope with the trauma of being taken away from his family and his country and taken in exile to America.”
Rev Love added: “If he is in this country his family could visit him on a weekly basis, he could telephone us on a daily basis, he will have the support of a chaplaincy and a prison service which is dedicated to the care of those with mental health issues.
“If he is taken to America he is going to be incarcerated in an American system which is not geared up for that kind of support.”
He acknowledged that his son should “face the music” if he had done wrong but said “it should be a British band”.
“If we have a special relationship with the United States they should trust us to deal with Lauri in an appropriate way.”
In September 2016 a district judge at Westminster Magistrates’ Court ruled that Love could be extradited. The High Court appeal centred on that ruling made by District Judge Nina Tempia.
Edward Fitzgerald QC, for Love, submitted there were “overwhelming reasons of justice and humanity” why any trial should take place in the UK.
He argued that it would be “unjust and oppressive” to extradite him because of his severe mental disorders.
Peter Caldwell, representing the US, made submissions inviting the judges to dismiss Love’s appeal.
In written argument he said the district judge’s conclusion on extradition was “reasonably open to her on the findings of fact she made”.
Having identified a high risk of suicide, she “properly assessed whether and how that risk could be managed were the appellant to be extradited”.