Some of May's officials think that quitting the customs union in order to win the power to strike free trade agreements with countries such as the USA or Australia is not as desirable as passionate Brexit supporters believe, Bloomberg reported on April 12.
The UK's parliament will vote on an official exit treaty at a later date, at which point it will have the power to veto any such agreement.
She said the Northern Ireland Office had been informed ahead of the visit.
Ministers have received a new warning not to allow Britain's withdrawal from the European Union to jeopardise the Good Friday Agreement.
Shadow foreign secretary Emily Thornberry, who also appeared on the program, said that remaining in a customs union "makes sense".
Last week's defeat, the first of two on that day, increased pressure on May to reconsider her refusal to remain in a customs union with the EU.
Northern Irish businesses have warned they can not accept any Brexit deal that would allow future imports of American chlorinated chicken as it would "all but guarantee" a hard border being set up by the EU.
The first - a "customs partnership" - would entail Britain mirroring European Union rules and collecting tariffs on goods heading for the bloc.
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A Downing Street source said Mrs. "I think we have got to win that case and that is my determination".
Davis said there was a "risk" that French or Dutch border checks would make life hard if no new system for smooth operations is ready to introduce - but he insisted he is talking to European Union governments about this issue.
Although that vote would be a symbolic and non-binding, it has the potential to deepen Tory wounds on Brexit.
The EU's chief negotiator, Michel Barnier, said everyone "knows where the EU stands" - adding that it is up to Theresa May and her government to come up with its vision for the future. "The prime minister is absolutely clear: we are leaving the customs union and will be free to strike our own trade deals around the world", he said.
Business, the European Union, and probably a majority of Parliament all want the U.K.to stay, but if May agrees to do so it could prompt a rebellion in her party that could end up with her being ousted.
It comes as the Government suffered three more heavy defeats in the House of Lords over its flagship Brexit legislation.
Ten Conservative peers voted against the government, including former deputy prime minister Lord Heseltine and the former ministers Lord Patten of Barnes, Lord Willetts and Lord Deben.
The government says the charter's rights are already covered by British law.
He said: "This Bill should not be used as an excuse to reduce the legal rights which we all enjoy against the state".