Mrs May's reply sparked concern among Conservative Brexiteers that the Prime Minister could concede too much ground to Labour in an attempt to win cross-party backing for a deal with Brussels.
The British government has agreed to allow citizens of Norway, Iceland and Liechtenstein already living in Britain to remain after Brexit even if the country leaves the European Union without a deal.
Mrs Leadsom said there was "no chance" Mrs May would adopt Mr Corbyn's "view of the world", adding: "The Prime Minister has been absolutely clear we're leaving the EU, we're leaving the customs union, we're leaving the single market".
Britain has signed a trade continuity agreement with Switzerland to avoid disruption for thousands of businesses post-Brexit, less than 50 days before the United Kingdom is due to leave the EU.
'So he wants a customs union and he is unclear as to whether that means he also wants an independent trade policy.
She added: "The fundamental negotiating challenge here is the EU's position that completely frictionless trade is only possible if the United Kingdom stays in the single market".
Brexit minister Stephen Barclay will meet European Union negotiator Michel Barnier on Monday ahead of a crunch moment in parliament on Thursday, when lawmakers will try to force May to change course or give up control of the exit process.
Mrs May has previously ruled out a customs union, which would restrict the UK's ability to strike trade deals, and could face Cabinet resignations if she changed her position.
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The call comes after Labour leader Jeremy Corbyn last week set out five conditions he wanted to see met before he would consider supporting Mrs May's Brexit plan.
DIT says that with the agreement the British vehicle industry, which has consistently warned against a no-deal Brexit, could avoid up to £8m a year in tariff charges on their exports that would apply if the agreement had not been reached.
Downing Street said Mrs May will make a Commons statement on the latest developments in the Brexit negotiations on Tuesday afternoon to give MPs more time to "digest the content" ahead of a series of expected Commons votes on Thursday.
In the meantime, Brexit Secretary Stephen Barclay has been meeting members of the Alternative Arrangements Working Group of Tories drawn from all sides of the party who have been seeking a compromise solution to avoid the need for the controversial backstop.
Mr Corbyn has repeatedly said there should be an election if Mrs May can not get a deal through Parliament and he has faced concerted pressure from some in his party to push for a second public vote.
She has said she wants to bring a revised deal back to parliament for a vote "as soon as possible" but has not yet set a date for doing so.
Jeremy Corbyn said he believes Theresa May might try to run out of the clock on a Brexit deal.
She'll say that if she hasn't brought them new deal by February 27, there will then be another opportunity to vote, Communities Secretary James Brokenshire confirmed in an interview.