David Davis has said securing temporary customs arrangements with the EU would be "in both sides' interest" as he insisted European leaders did not want to punish Britain for voting to leave the bloc.
The Brexit Secretary will publish proposals on Tuesday morning, outlining plans for a time-limited transition which would ensure businesses on both sides of the Channel only have to adapt once to rule changes.
Temporary arrangements could allow trade deals to be negotiated with other countries while governments and businesses adjust to new arrangements.
However, reports suggested this would have to be negotiated during Brexit talks, with members of the EU's customs union barred from striking their own trade deals outside the bloc.
Mr Davis told ITV's Good Morning Britain: "We sell them, the Europeans, about 230 billion euro of goods and services a year. They sell us 290 billion euro. So there are a lot of things there."
Asked whether Britain would have to pay to stay in the customs union, he said: "Well, I don't think ... well, what happens in that sort of interim period you will have to leave me to negotiate, I'm afraid, how we do it, but the aim is to bring to an end these huge £10 billion-a-year payments, bring that to an end now.
"We are still haggling with them over what we may owe them in the short term but we are going to bring the overall thing to an end.
"This is something that is in both sides' interest. Now you are right, there will be political pushback and that's what the negotiations will be about."
Mr Davis said the negotiations were going "fine" and he "wouldn't have taken the job" if he was not confident of achieving a good deal for Britain.
He said: "The simple truth is we want to come out of this better but they (the Europeans) want to come out of it better too.
"There was a terror early on that we would be the first of many countries breaking off.
"After the victory of (President) Macron in France, that terror is reduced.
"They are no longer quite so afraid so the punishment battalion side is now reducing."
The proposals for new customs arrangements to allow trade with the EU are being outlined in the first of a series of "future partnership papers" being released by the Government.
One option being put forward by Mr Davis for new arrangements would see the UK manage a new customs border with administration streamlined to the "fullest extent possible".
The Brexit Secretary will also float plans for a customs partnership with the EU which would negate the need for a customs border between the UK and the rest of the bloc.
Mr Davis played down suggestions of Cabinet splits over Brexit following reports of infighting between different ministers on the approach to the critical negotiations.
He told the BBC Breakfast: "Of course there are different views on elements of the deal because departments have their own specific interest.
"Treasury is obviously concerned about the City; Business Energy and Industrial Strategy is concerned about things like research and manufacturing. They have their different fields; Liam (Fox) wants to do his trade deals, my job is to make sure that we do all of those in a practical way that works and also in a way that is negotiable and we can get that outcome that we want so we are not pitching for the moon.
"Of course there are discussions, of course there are interests, but we all want the best outcome for Britain."