Some Liberal MPs expect voters to back fixed four-year federal parliamentary terms after Labor leader Bill Shorten resurrected the idea.
The opposition leader believes the change - already in place in most states and territories - will allow governments to be more daring and determined because they're not focused on the next election.
The prime minister phoned Mr Shorten after he floated the proposal during a Sunday television interview, with Mr Turnbull indicating he was prepared to discuss the suggestion.
"In the last 24 hours I think there's real appetite for genuine reform which is bipartisan," the Labor leader told reporters in Melbourne.
"I think (Mr Turnbull) supports four-year terms. I support four-year terms. Why don't we look at how we can make this work in the interests of Australians."
Mr Shorten said he thinks Australians are fed-up with going to the polls every two-and-a-half years, but insisted a referendum on indigenous recognition should be the priority.
Cabinet minister Steve Ciobo expects the public to be broadly supportive, but acknowledges some issues would have to be considered more closely.
"Let's just let the community have a think about it, have a chat about it if they'd like to and if there's opportunity for us to look at it so be it," he told Sky News.
Liberal colleague David Coleman earlier this year flagged a private member's bill to establish fixed four-year terms.
He hopes a referendum can be held at the next federal election.
"It would mean more certainty for business in terms of business investment," he told ABC radio.
Frontbencher Kelly O'Dwyer is open to the discussion but warned there were two sides to the argument.
"If you have fixed terms you can either entrench good governments or bad governments," she said.
Nowadays the prime minister has the power to decide when an election will be, and the average term in between has been about two-and-a-half years.
Treasurer Scott Morrison was also sceptical, insisting it's not a top priority for the coalition.
"I don't think Bill Shorten should be given three years let alone four," he said.
One hurdle has been the assumption moving to four-year terms would be matched with a corresponding change to elect senators for eight years, but Mr Shorten said that shouldn't be a "deal-killer".
Deputy Prime Minister Barnaby Joyce, previously a senator, is open to the idea which he says has been knocking around for a while.
Asked whether an eight-year term in the upper house would be too long, he told reporters in Canberra: "I was there for eight years, seven months and a day. What do you reckon?"
