Ballot papers and pencils could be stored away permanently with Malcolm Turnbull and Bill Shorten both suggesting a change to electronic voting.
The prime minister has long advocated electronic voting and the opposition leader will write to him this week to offer bipartisan support.
"We're a grown up democracy, it shouldn't be taking eight days to find out who's won and who's lost," Shorten said while conceding the election on Sunday, a week after polls closed.
"I take nothing away from the professionalism of the Australian Electoral Commission, but it's the 21st century."
After each federal election a cross-party parliamentary committee examines possible changes to electoral laws.
In November 2014 then-chair of that committee Tony Smith reported that after considering electronic voting in detail he had changed his mind to oppose it.
"Australia is not in a position to introduce any large-scale system of electronic voting in the near future without catastrophically compromising our electoral integrity," the Liberal MP, who is now Speaker, said at the time.
The counting of votes from July 2 is taking the usual amount of time, in line with legal requirements, but there are many close races which make the result less clear-cut than most elections.
The prime minister pointed to the New South Wales iVote system as an example of how to implement electronic voting.
"Yes this is something we must look at," Turnbull said. "I'm absolutely -- that's been a passion of mine, or an interest of mine for a long time."
Last year, around 19,000 people voted using the NSW system before an error was spotted that had removed the group voting boxes for the Outdoor Recreation Party and the Animal Liberation Party.
"There was no fault on the computer systems per se; it was a human error in data entry," New South Wales Electoral Commission (NSWEC) CIO Ian Brightwell told ZDNet at the time. "Unfortunately, at the time of going live, we didn't have an opportunity to view the ballot paper."
A month prior, a pair of security researchers found the analytics service used by iVote left voters vulnerable to having their ballots changed, as well as having the iVote site open to the FREAK attack.
However, the NSWEC said the researchers' claims were overstated.
Brightwell questioned the researchers' motivation for releasing their findings only a week prior to the state election.
The iVote system was originally implemented ahead of the 2011 state election for vision-impaired voters and those living in rural areas who have difficulty reaching polling places. Its use was later expanded to cover pre-polling.