Former prime minister Lord David Cameron has changed his mind and backed the bill, after previously being opposed to assisted dying.
Lord Cameron said he believed the current proposal was "not about ending life, it is about shortening death".
Previously his main concern had been that "vulnerable people could be pressured into hastening their own deaths", but he said he believed the current proposal contained "sufficient safeguards" to prevent this.
Lord Cameron is so far the only ex-prime minister to support the bill after Gordon Brown, Baroness Theresa May, Boris Johnson and Liz Truss all said they were against it.
Prime Minister Sir Keir Starmer backed assisted dying when it was last debated in Parliament in 2015 - but has not revealed how he will vote this time round.
Asked whether his view on the matter had changed, he told a Downing Street press conference: "The vote is coming up... obviously the government is neutral on this and it is a genuinely free vote for all members of Parliament and I don't want to put pressure on them.
"I've obviously got a huge amount of interest and experience in this."
In his former role as director of public prosecutions, Sir Keir changed legal guidance to make it less likely that people motivated by compassion to help someone die would face prosecution.