S Kidman and Co. is Australia's largest privately-held landholding.
Founded in 1899, its properties cover 101,000 square kilometres across three states and the Northern Territory.
That's a little over one per cent of Australia's entire land mass and about 2.5 per cent of its agricultural land.
Earlier this year, a bid from a Chinese-led consortium was blocked by Treasurer Scott Morrison, who argued such a huge stake in foreign hands may not be in the national interest.
But now, four local families with extensive livestock and transport operations have put forward a $386 million bid.
Tom Brinkworth, Sterling Buntine, Malcolm Harris and Viv Oldfield say under their offer, Kidman would stay completely Australian-owned.
Mr Buntine has told ABC News Kidman's cattle herd would triple in size.
"It virtually takes Kidman from having a supply chain of what one would call a medium-sized beef producer in Australia to having one of the largest herds in the world underneath the brand."
Former Liberal leader John Hewson has told Sky News the offer would come as a relief to the Turnbull government.
"I wondered, in fact all the way through, why we hadn't had a significant Australian bid. It's an iconic set of properties and I'm surprised that we hadn't seen one. So it's a good thing and it may not be the last we hear of this because there may be counter-offers and counter-bids, but it would be a sigh of relief in Canberra I think right now."
The bid trumps one made earlier this month by Australia's richest woman, Gina Rinehart.
She's offered $365 million to control 67 per cent of the empire while a Chinese partner, Shanghai CRED, would hold the remaining third.
It may be an Australian-majority bid but it would still require approval from the Foreign Investment Review Board.
China's business interests in Australia have become a contentious issue in Canberra despite a report released last month showing China is only the fifth-highest foreign owner of agricultural land in Australia.
Former Labor government minister, Craig Emerson, has told Sky News the Rinehart bid still deserves careful consideration.
"I would not like to see the Rhinehart bid, which does actually involve a Chinese partner, effectively being discounted or in some way compromised because of the very fact of a Chinese partner."
The political sensitivity has seen Ms Rinehart's offer exclude buying an area close to the Woomera weapons-testing range.
As a result, she argues the real difference between the two bids is no more than $2 million.
In the past, Deputy Prime Minister Barnaby Joyce has been a vocal critic of China's push for Australian land.
But he's also argued that foreign ownership is important to Australia.
"One of things Australia offers is free title of land: it underpins our democracy, it underpins the rights of the Australian people as well. We are not scared of foreign investment, we are built on foreign investment. It is a balancing act though, nothing is a binary argument where one thing is absolutely beyond questioning and never to be even [mentioned]. We have to do all things in moderation and in all things with proper oversight."
The Kidman board is required to consider any offer that's bigger than the one on the table.
Ms Rinehart and her associates also have a right to match any rival bid should their syndicate gain foreign investment approval.
