In comments reported by The Telegraph, Prof Hawking told O’Briain, who himself as a degree in theoretical physics: “To keep someone alive against their wishes is the ultimate indignity.
“I would consider assisted suicide only if I were in great pain or felt I had nothing more to contribute but was just a burden to those around me.”
However the 73-year-old added: “But I’m damned if I’m going to die before I have unravelled more of the universe.”
Hawking has previously spoken out in support of assisted suicide for people suffering from terminal diseases.
In 2013 the cosmologist told the BBC: “We don’t let animals suffer so why humans?
He said: "I think those who have a terminal illness and are in great pain should have the right to choose to end their lives and those who help them should be free from prosecution.
"But there must be safeguards that the person concerned genuinely wants to end their life and they are not being pressurised into it or have it done without their knowledge or consent, as would have been the case with me."
In his latest interview, Hawking also talked of the isolation his condition sometimes leads to.
He told O’Briain: “At times I get very lonely because people are afraid to talk to me or don’t wait for me to write a response.
“I’m shy and tired and times. I find it difficult to talk to people I don’t know.”
When asked what he missed about being able-bodied, he replied: “I would like to be able to swim again. When my children were young, I missed not being able to play with them physically.”
Prof Hawking was diagnosed with his disabling and incurable condition aged 21 and told that he had just two or three years to live.
Following a bout of pneumonia in 1985, he was placed on a life support machine which his first wife, Jane Hawking, had the option to switch off.
Recovering from the disease, Prof Hawking went on to complete his popular science best-seller A Brief History of Time, which sold more than 10 million copies worldwide.
Only 5% of people with the kind of MND he has - called amyotrophic lateral sclerosis (ALS) or Lou Gehrig's disease - survive for more than a decade after diagnosis.
Referring to euthanasia in 2006, he said: ''The victim should have the right to end his life, if he wants. But I think it would be a great mistake.
"However bad life may seem, there is always something you can do, and succeed at. While there's life, there is hope.''
The full interview “Dara O’Briain meets Stephen Hawking” will be broadcast on BBC One on 16 June at 22.35.