Rugby Australia has offered to host this summer's British and Irish Lions series against South Africa.
The Lions are due to visit South Africa in July and August with a three-Test series against the world champions.
But issues around Covid-19, including the emergence of a new variant in South Africa, has led to uncertainty over the viability of the tour.
"We're here to help," Rugby Australia chairman Hamish McLennan told the Sydney Morning Herald.
"What we learnt from the Tri Nations last year and the tennis that's happening now is that Australia can successfully stage global tournaments in a Covid world.
"It's particularly tough in the UK and South Africa at the moment and I believe the more international rugby that gets played here, the better."
McLennan says profits from the tour would be split between the Lions and South Africa, with Rugby Australia covering their costs.
The Lions board have been discussing contingency plans in the event the trip has to be abandoned, including the possibility of hosting games in the UK and Ireland.
Crowds have returned to watch live sport in Australia, with up to 30,000 fans allowed to watch next month's Australian Open in Melbourne.
Analysis
BBC Rugby Union correspondent Chris Jones
This is a fascinating development, and while it has been described as a "long shot" by a well-placed source, it has certainly not been dismissed by either the Lions or South Africa, and is another contingency plan being actively explored.
The pros of this are clear: it would protect the touring ethos of the Lions and would ensure the best possible chance of getting supporters in the grounds - which would be a huge boost - while there is also the tantalising prospect of the Lions playing a warm-up Test against the Wallabies, or even France, who are touring Down Under this summer already.
But there are major obstacles too, both logistical and financial. And with it being unlikely that supporters from the UK and Ireland will be able to flock to Australia - with tight border controls set to be in place for most of 2021 - the atmosphere and energy around the tour will be in the hands of the Australian rugby public, which has been somewhat apathetic in recent years.