The agreement could see Britain remain within the EU's common external tariff until a future customs arrangement is ready in a temporary fix created to avoid a massive jolt for business and a hard border in Northern Ireland.
Downing Street reportedly believes the proposal would allow ministers to say they have formally left the EU customs union while avoiding a cliff-edge scenario for business in Northern Ireland and the emergence of a hard border with Ireland.
May added fuel to those rumours on Wednesday when she told MPs that the United Kingdom government is now aiming for a "future customs union" with the EU.
The EU believes that "Max Fac" can not be the solution to the border problem, but contrary to some reports it has not killed off May's customs partnership idea, mainly because it allows a hybrid form of customs cooperation.
HuffPost UK understands that Brussels sees serious problems with the plan, including the risk that exemptions would lead to a growth in small firms that could avoid strict European Union rules on standards on everything from toy safety to pesticide strength.
There are doubts over whether the European Union would accept a time-limited arrangement, as this would mean Britain could, in theory, drop out of the EU's customs arrangement without a solution for the Irish border in place.
"Basically it's keeping [Britain] in the external tariff until the new system is ready", the official said.
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To soothe concerns of Brexiteers, it would include a "sunset" clause ensuring Britain does leave in the end. Both sides would need this.
"There is no doubt that a customs partnership hybrid model makes the Irish border situation easier, there is no doubt that the question of the Irish border is resolved by the customs partnership in an easier way than maximum facilitation".
Crucially, the prime minister's so-called Brexit war cabinet has already nominally approved the plan, according to Bloomberg and the Telegraph, which reported that ministers signed off on the plan despite objections from Foreign Secretary Jonson and Environment Secretary Michael Gove.
May's Conservative Party defeated Labour by 301 to 269 votes, handing the government a victory in a parliament equally divided over the terms of Britain's divorce from the European Union and their future customs arrangements.
One source said: 'It's about providing an alternative to the EU's border down the Irish Sea'.
At home, May has to balance the demands of Brexit supporters against those ministers who want to keep the closest possible ties to the EU, and any hint that Britain could stay within the customs union has become a flashpoint. "We have said there will be no ANPR [automatic number plate recognition] cameras, no new cameras, we have been clear that there will be no new physical infrastructure", Bradley said. The horizon seems to be unreachable. People voted to leave, they did not vote for purgatory'.