The bill could come up for its first reading before the September 23 election, but Mr Seymour expects there will be delaying tactics by MPs who don't want to take a position on it ahead of the election.
An important factor in the timing is the imminent report on public attitudes to voluntary euthanasia that a parliamentary committee is preparing.
The report, the result of a two-year inquiry, will have an impact on the debate around the bill and could influence the attitude of some MPs.
If the bill does get through its first reading it will go to a select committee for public submissions - which will take at least six months - and then have to survive three more stages in Parliament.
An opinion poll taken in June 2015 showed 71 per cent of New Zealanders supported voluntary euthanasia.
Mr Seymour's bill gives people with a terminal illness or a "grievous and irremediable medical condition" the option of requesting assisted dying.
Assisted dying has been debated twice before by Parliament and defeated at first reading, in 1995 and 2003.
- NZN