Noel Conway, 68, had his bid for a judicial review of the law on assisted dying rejected in October last year.
Mr Conway, supported by Dignity in Dying, had instructed law firm Irwin Mitchell to bring the case to fight for his right to have the option of an assisted death when he is in his final six months of life.
Now an oral hearing is due to take place on Thursday at the Royal Courts of Justice to determine whether the October judgment can be appealed.
Speaking after the October decision was confirmed Mr Conway said: "I am told the only option I currently have is to effectively suffocate to death by choosing to remove my ventilator, which I am now dependent on to breathe for up to 22 hours a day.
"There is no way of knowing how long it would take me to die if I did this, or whether my suffering could be fully relieved. To me, this is not choice – this is cruelty.
"This decision denies me a real say over how and when I will die.”
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Mr Conway added: "Knowing I had the option of a safe, peaceful assisted death at a time of my choosing would allow me to face my final months without the fear and anxiety that currently plagues me and my loved ones.
"It would allow me to live the rest of my life on my own terms, knowing I was in control rather than at the mercy of a cruel illness.
"Throughout this case I have been overwhelmed by the outpouring of support the public has shown me. I know that this fight is important not just to me, but thousands of others.”
Mr Conway's case was opposed by the Secretary of State for Justice, with Humanists UK, Care Not Killing and Not Dead Yet UK also making submissions.
His legal team said he will not be attending the appeal hearing as he is too unwell.