Voters could go to the polls in two federal elections next year under a radical proposal that could buy the Morrison government more time to win back support.
A general election in May remains the most likely scenario.
But some coalition MPs are open to holding a Senate election early in 2019 and a separate election for the House of Representatives several months later, Fairfax Media reported on Tuesday.
However, others have dismissed the dual election idea, with one government source telling Nine Network it was "fanciful".
Prime Minister Scott Morrison is spending the week touring marginal LNP seats on Queensland, in what is widely considered a soft-launch of his federal election campaign.
Asked on Monday whether his four-day bus tour amounted to a quasi campaign, Mr Morrison replied: "This is me doing what I do. I'm out, I'm listening, I'm hearing and I'm doing. That's what I'm doing as a prime minister."
The prime minister will visit the Sunshine Coast on Tuesday, while Opposition Leader Bill Shorten attends the Melbourne Cup carnival at Flemington.