Image copyright EPA Image caption No 10 are remaining tight lipped about the PM's Florence speech

No sooner had her next European adventure been confirmed than the speculation began.

What message will Theresa May take with her to Italy next week? Inside Number 10, the view is not to spill a single fagiolo, a bean, before the words come out of her mouth.

That's not just because they want the story to be told on her own terms in her own words, when she is ready to tell it.

But also, perhaps, because I'm told that she is yet to have signed off the full contents with those members of the cabinet who might object to some of it.

And frankly, at this stage, it is extremely difficult to get to the bottom of what the precise thinking in government really is, about the next move on Brexit.

And it is also very hard to understand exactly what the views really are from the different parts of the EU machine.

In the coming days, I'm told Boris Johnson is likely to see the PM. She'll try to square him on her plans, with private suggestions that she has to persuade him to accept cash going to Brussels.

That would go against, of course, what he suggested in the referendum campaign, and also how he evoked the memory of Margaret Thatcher earlier this year, by mentioning the "illustrious precedent" of Fontainebleau.

Image copyright Getty Images Image caption Can the PM win over Boris Johnson to the idea of continued EU payments?

I'm told Theresa May has not yet put a proposal to the foreign secretary that would involve continued payments to the EU during a transition period for a couple of years after the UK leaves the EU, or to other Brexiteers.

"She has yet to try it on for size with these people", I was told. And sources suggest it will be hard for Mr Johnson to stomach in particular. "I can't see him turning and agreeing that's palatable," one source said.

The prevailing wind however in the cabinet, as the chancellor even said publicly this week, is for a transition period that looks rather similar to the status quo, and to retain some of those privileges -and burdens - would have to involve some payments.

In fact, there are whispers that UK officials are ready to put just such an offer on the table.

Fee for access?

Previous speculation seems to be solidifying around a potential "sensible offer" where the UK would offer to pay £10bn a year for three years, in return for continuing access to the single market, while business disentangles itself from the EU and the final details of a permanent trading relationship are hammered out.

That would seem a specific price for a specific outcome, a fee for access, rather than one enormous Brexit bill. Under this plan, the longer term liabilities of the UK to EU pensions, and other assets, would be settled over time by committees, with the political sting removed.

Image copyright Reuters Image caption Are the remaining EU countries totally united in their approach to Brexit?

But it's not just confirmed Brexiteers who might find that hard to accept. Whispers suggest that while France and the EU Council would accept that broadly as a fair deal, Germany and the EU Commission see that as not good enough.

A UK government source tells me that, on the issue of the bill, France and Germany are split. It's not clear however what the view is of the EU chief negotiator, Michel Barnier.

But remember his mandate comes from the member states, he is unable to make compromise decisions on his own.

Divisions inside "the 27" are denied in Brussels, where they are described as "wishful thinking" by the UK.

Here, the speech is so sensitive no one will be drawn on the record. But one former diplomat, familiar with the talks, told me there is a chance for the UK to throw the EU "into disarray" - put forward that "sensible offer" and destroy the unity the 27 other countries have worked so hard to preserve.

That could in theory, in turn, crack open the impasse in the talks and give the UK the advantage.

The Florence speech has the potential perhaps to be a game-changing moment in this vital process.

But could Theresa May's cabinet stomach the offer that might finally open up a British advantage?