British Prime Minister Theresa May is expected to give more details on her vision for Brexit later.
She is giving a speech in Florence, Italy where she will call on both sides to make the UK's departure from Europe work 'smoothly and sensibly'.
She will also call for "creativity" in what is "inevitably, a difficult process".
Her intended audience in the Tuscan capital - the leaders of the EU27 nations - will not be there in person.
But Mrs May will appeal to them by offering to fulfil UK commitments in the existing EU budget round until the end of 2020, even after Britain formally leaves the bloc in March 2019.
That equates to a "financial settlement" of at least €22.6bn, and perhaps more, though no number will be used.
In return, she will accept a time-limited transition period, which will essentially keep the same existing rules and market access in terms of the single market and customs union for a period of about two years until 2021.
This has been a key demand of many UK businesses in recent weeks, and most British cabinet ministers.
'In all of our interests'
She is expected to remind leaders of their "profound sense of responsibility" to ensure a smooth Brexit and in establishing a new economic and security partnership.
She is expected to say: "If we can do that, then when this chapter of our European history is written, it will be remembered not for the differences we faced, but for the vision we showed; not for the challenges we endured but for the creativity we used to overcome them; not for a relationship that ended but a new partnership that began.
"While the UK's departure from the EU is inevitably a difficult process, it is in all of our interests for our negotiations to succeed.
"So I believe we share a profound sense of responsibility to make this change work smoothly and sensibly, not just for people today but for the next generation who will inherit the world we leave them.
"The eyes of the world are on us but if we can be imaginative and creative about the way we establish this new relationship."
Mrs May will be arriving with a large entourage, including her Cabinet ministers who have already read the speech.
While there she is expected to face protests from British citizens resident in Italy, who have been campaigning alongside EU citizens in the UK for stronger guarantees of existing rights after Brexit.