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He has been diagnosed with several psychological disorders and claims to be suffering from serious kidney and heart conditions.
He contacted Exit Switzerland, a organisation which supports people through assisted suicide, in 2018 and argues that he should be eligible.
"It would be better to be dead than to be left to vegetate behind these walls," he told AFP.
The law in Switzerland allows euthanasia but bans assisted suicide performed with "selfish motives", with most assisted suicides being performed on elderly people suffering from terminal diseases.
Authorities aim to decide on Vogt's request this year, asking the Swiss Centre of Expertise in Prison and Probation, a publicly funded foundation, to offer advice.
The centre has previously found that prisoners should be allowed to end their own lives, as long they have "a physical or mental illness resulting in unbearable suffering", Barbara Rohner, lead author of the report, told AFP.
Vogt said that he wanted to die because of his deteriorating quality and his inability to see his sick mother.
He told the Blick newspaper that he wants to end his life on his 70th birthday, August 13.
Some have expressed concern about Vogt's claim, saying that the technique could be used as leverage for better prison conditions.
A spokesperson for a Swiss victims' rights group said the decision on a prisoner's right to die should ultimately belong to their victims.