Mr Conway, from Eaton Constantine, near Shrewsbury, who has motor neurone disease, has become a national figure in the campaign to remove the ban on assisted dying in the UK.
The agreement by Mr Hancock to have an online meeting with the 70-year old, was made in the House of Commons on Thursday, when he announced that people would be able to travel abroad during the November lockdown for the purpose of assisted dying.
He said that how to best support people in their choices at the end of their life was a complex moral issue.
During the Parliamentary debate, Shrewsbury and Atcham MP, Daniel Kawczynski asked the health secretary to talk with Mr Conway about the wider issue of having to travel abroad to avoid breaking UK law.
He said: "I think it's very difficult to tell somebody who is in pain and suffering and who wants to die that the state is going to prevent them from doing that. As a Roman Catholic, I have recently changed my mind on this issue because of my constituent Mr Noel Conway who lives near Shrewsbury.
"I said to him, 'Why don't you go to Switzerland?' And his answer will stay with me forever: 'No, I'm an Englishman, I want to die in England.' And I think it's extremely important that our citizens have this right.," he said.
Mr Hancock said he was happy to have the meeting and speak to Mr Conway.
"The compassion of the case can not be understated. We have to respect all members of this house who have deeply held views.We should ensure that there is a debate about this and that it is done in an evidence based, sensible and compassionate way."
Earlier in the debate Mr Hancock said: "Travelling abroad for the purpose of assisted dying is a reasonable excuse and so anyone doing so would not be breaking the law. The question of how we best support people in their choices at the end of their life is a complex moral issue that, when considered, weighs heavily upon us all."
Under current law, based on the Suicide Act 1961, it is an offence to encourage or assist the death of another person. However, it is legal to travel abroad for the purpose of assisted dying where it is allowed in that jurisdiction.
Mr Conway, 70, a retired college lecturer relies on a ventilator to breath.
He went to the Supreme Court in 2018 calling for a judicial review on assisted dying.
Earlier this year he said increasing numbers of people who were suffering because of their health conditions, who may or may not be within six months of dying, were demanding the right to a civilised exit to their lives.
"Those who have the money and are still capable of transport are taking the option of going abroad to Switzerland. But for those without the means or capacity, they must continue to suffer at end-of-life," he said.
Today Mr Hancock said the pandemic had made care for people at the end of their lives a central issue of public debate.
"We of course do acknowledge the changing views of many, including many in the medical profession, and of course we observe the changes and the international debate that is taking place.
"I think it is absolutely reasonable for this House to have a conversation and a discussion on what is an important topic.