Murdoch's London-based global news hub
"You're not having BSkyB on the cheap."
That was the rather stark message that BSkyB's board gave to News Corporation this weekend, when it first offered 675p a share to buy the 61% of the company that it doesn't already own and then increased the offer to 700p - which would value the whole of Sky at £12.2bn.
BSkyB's board and its advisers believe the business is worth around £1bn more, or greater than 800p per share.
So what happens, now that BSkyB has rebuffed the initial bids?
Well, News Corporation will press ahead with the process of trying to buy Sky by initiating the process of having the European competition regulator scrutinise the deal.
One interesting question is whether British regulators, the Office of Fair Trading and Ofcom, and the British government will want to repatriate scrutiny of the deal, as they have the right to do.
Some may think David Cameron, the prime minister, will want to be a million miles from any adjudication on Sky's commercial ambitions, given that he was perceived to have benefited greatly during the general election campaign from the enthusiastic support he received from Rupert Murdoch's Sun newspaper.
But his Liberal Democrat partners, who have traditionally been critics of the media clout of Mr Murdoch, will be in something of a quandary.
Because they'll be aware that in media deals of this size and importance, the government has the right to intervene on public interest grounds.
Vince Cable, the business secretary, will probably not wish to be seen to be wimping out of having a voice on a takeover that would profoundly change the media landscape in the UK.
The takeover would erase any scintilla of doubt that Mr Murdoch's News Corporation would be the most powerful of all the traditional media groups in the UK. Only Google would perhaps be as influential.
The combination of Sky with his newspapers, such as the Sun and the Sunday Times, would generate annual revenues of around £8bn, compared with the £4.6bn income of the next largest player, the BBC.
For me, the fascinating aspect of it all would be in the news arena.
It would put Sky News together with Mr Murdoch's newspapers and - very importantly - his new venture in putting their online versions behind a so-called pay wall.
The opportunities for cross-promoting those newspapers on Sky will be seen by other newspaper groups as giving News Corporation a huge advantage.
And in a world where digital convergence is a reality, not blue-sky waffle, they'll also be fearful of the potential of marrying Sky's pay-TV platform with News Corporation's pay-for-news platform.
As for James Murdoch, the heir apparent to Rupert Murdoch, he would sit in the middle of a unique media hub located in London.
He would become arguably the single most powerful figure in European media, huge in pay TV - in the UK and Italy - and massive in news.
Update 11:30: The likelihood must be that eventually News Corporation and BSkyB will agree a price for the 61% of Sky that News Corporation doesn't yet own.
The tone of their statements this morning suggests an intent to marry.
More interesting therefore will be the attitude of regulators and politicians.
As it happens, British regulators - Ofcom and the OFT - already treat Sky as effectively controlled by News Corporation.
That's absolutely clear from their regulatory actions over the past few years.
So in theory the change to 100% ownership would not represent a hugely significant event for them.
But that's to ignore one important consequence of the deal: News Corporation would be able to get its mits on Sky's £1bn plus of annual EBITDA cash flow.
At a time of severe financial difficulties for most newspaper groups, access to all that cash would reinforce the market strength of News Corporation's formidable array of titles - notably the Sun, the Sunday Times, the Times and the News of the World.
Arguably therefore the competitive landscape in news would tilt further to the benefit of the Murdochs.
Maybe that won't be significant enough to worry regulators either in Brussels or the UK.
But, as I mentioned earlier, it will alarm some politicians - including those Lib Dems, now members of the government, who were horrified by how the Sun lampooned Nick Clegg in the closing stages of the election campaign (before Mr Clegg became the best chum of D Cameron, the Sun's preferred candidate to head the government).