Housing and Communities Secretary Sajid Javid echoed the sentiments on Sunday, tweeting that leaving the customs union was an "intrinsic part" of leaving the EU.
Downing Street aides have also reportedly put bets on which member of the cabinet would be first to resign if May U-turns on the customs union, with Liam Fox and Boris Johnson the current favourites.
"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.
"It's been the CBI, Brussels, and all the those who want the status quo, because the status quo benefits them, they don't want a solution in our on the Irish border".
Common external tariffs are applied to goods imported from countries from outside the bloc.
Labour MP Chuka Umunna and backbench pro-Remain Tory Anna Soubry have tabled amendments to the Trade and Customs Bill that will make staying in the customs union a legal objective of the government.
Hardline Brexiteer Conservative MPs have privately warned the prime minister that any further retreat on Brexit could lead to an attempt to topple her.
Armenian president accepts resignation of government
After the 2008 presidential vote, 10 people died in clashes between police and supporters of the defeated opposition candidate. Mr Sargsyan stressed that he and all the countrymen expect that no need for a state of emergency will ever arise in Armenia.
Questions on the Customs Union arise as the EU rejects the UK's proposals for the Irish border after Brexit.
Senior euroskeptic ministers are likely to make their case for breaking free from European Union rules directly to the prime minister on Wednesday, when she holds a key meeting of her inner Cabinet focused on the Brexit negotiations, Tim Ross reports.
The EU has rejected all the United Kingdom government's suggestions up to now.
Peers voted by 348 to 225 in favor of a plan requiring ministers to report on steps to negotiate a continued union last week.
A showdown is expected to come at a meeting of the Cabinet Brexit committee scheduled for Wednesday when the trio will tell the PM that the "customs partnership" would be unworkable, the report said.
In comments released beforehand, he said: "We will work with old allies and new partners across the world, utilising the UK's economic strength and diplomatic prowess to forge new trading relationships".
"Ultimately, our task is to remove the unnecessary regulation, bureaucracy and red tape that inhibit the free trade in services".
Following the reports, angry ministers hit back last night, with Housing Secretary Sajid Javid tweeting that the British people had given "clear instructions" through the European Union referendum.