The Times said Brexit Secretary David Davis, International Trade Secretary Liam Fox, and Foreign Secretary Boris Johnson were concerned this would "encourage Brussels to press for Britain to stay in a customs union after Brexit".
The dilemma facing May is how to avoid physical infrastructure on the border between Northern Ireland and the Republic while Britain is outside the customs union and single market.
"We don't think staying in a customs union is the right thing to do and it isn't government policy to do so", a Downing Street source said.
And with a debate over Britain's membership to the customs union scheduled to take place in the House of Commons on Thursday, there were plenty of MPs happy to chime in with the business leader.
The EU Withdrawal Bill debate will inform the biggest battle over Brexit, expected in October or November, when lawmakers vote on the final deal negotiated with Brussels.
"You can't be in the customs union and have your own free trade deals".
We're not going to be part of the customs union or a customs union.
The Sunday Times reports that Downing Street has privately admitted the Prime Minister may have to accept some form of customs union with the EU. "That position hasn't changed and Downing Street have been clear about that this morning", he said.More news: Montana, Wyoming runners race to finish at Boston Marathon
More news: Commonwealth leaders agree to make Prince Charles head
More news: Smallville star accused of recruiting women for sex with self-help guru
Labour has called for the United Kingdom to join a new customs union post-Brexit, saying it would leave the current one but negotiate a treaty afterwards that would "do the work of the customs union".
This would likely enrage Brexiteers, with No.10 reported to believe that global trade secretary Liam Fox and foreign secretary Boris Johnson could resign. Staying in the customs union would nearly certainly prompt pro-Brexit lawmakers to submit letters calling for a leadership vote.
Mr Wilson said it would be "very unwise for the prime minister to show any sign of weakness" to European Union negotiators.
"Businesses know that crashing out of the Customs Union will be a catastrophe for jobs and employment in this country, but the Government seems determined to drive us off the cliff regardless".
Lawmakers will have to decide whether to back the government or reject the agreement - with the risk that Britain could crash out of the European Union next year without any deal in place.
In February, Kerr was a signatory to an ERG letter calling for "full regulatory autonomy" insisting the the United Kingdom should not be a "rule taker without any substantive say in whatever Brussels decides".
Those in favour of remaining in the customs union argue that cutting trading ties would severely damage the United Kingdom economy.
The Irish border is a key element of their case.