Parliament is set to hold a non-binding vote on the customs union on Thursday.
A source familiar with the discussion told the paper: "The discussion focused on what to do if parliament votes to stay in a customs union".
Yet John Redwood, the Tory backbencher, said on Monday he did not feel that Downing Street's reiteration of the plan to leave any form of customs union had been necessary.
However, Downing Street insists that she remains committed to cutting customs ties with the EU.
Mrs May is against remaining in the customs union, and has pledged that the United Kingdom will not be part of the bloc's single market after Brexit.
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Mrs May last week suffered a defeat at the hands of peers in the House of Lords when they backed an amendment to compel ministers to explain what they have done to ensure that Britain can remain in a customs union after leaving the EU.
BBC assistant political editor Norman Smith said Downing Street's move was an attempt to reassure Brexiteers anxious about a U-turn following the Lords defeat and pressure from the EU.
Communities Secretary Sajid Javid tweeted that the referendum gave "clear instructions" to leave the customs union and accused some of seeing it as a "kind of post-Brexit comfort blanket". His euroskeptic cabinet colleague, Liam Fox, the global trade secretary, is also a passionate advocate for leaving European Union common tariffs and commercial policies.
Mr Wilson said it would be "very unwise for the prime minister to show any sign of weakness" to European Union negotiators.
Umunna said on Twitter: "The Brextremists threaten May with a leadership election if she concedes on the customs union but a new Tory leader would face the same Parliamentary arithmetic".
"The only thing that will save her now is if she makes clear that there will be no more backsliding", one member of the anti-EU grouping the European Research Group led by Jacob Rees-Mogg told Business Insider earlier this year.
The EU has rejected all the United Kingdom government's suggestions up to now.
Those in favour of remaining in the customs union argue that cutting trading ties would severely damage the United Kingdom economy. The second, known among civil servants as the "maximum facilitation" option, would seek to minimise but not totally eliminate checks on the Irish border.