However, he says there are still some big differences left to resolve.
British negotiators in Brussels are thought to be preparing to sign up to a draft of the backstop for Northern Ireland - aimed at preventing a hard border - that could see the whole of the United Kingdom effectively inside the customs union.
She reportedly pitched her solution to the Northern Ireland "backstop", a major sticking point in the negotiations that has bitterly divided her party and caused friction with the EU.
Sky News understands work to prepare for such a scenario is already under way, while Brexit Secretary Dominic Raab has said he is confident Britain would be able to negotiate such agreements with the likes of France, Belgium and the Netherlands.
"What we can not do is see the United Kingdom locked in via the backdoor to a customs union arrangement which would leave us in an indefinite limbo - that would not be leaving the EU", he said on Friday.
"We can't accept a time limit, but we can accept it will only be there unless and until something better is agreed in the future, which is what everyone wants".
She said: "I am completely supportive of the prime minister".
While highlighting the DUP's confidence and supply agreement with the Conservative government at Westminster, Mr Coveney warned of an "imbalance" being created in Northern Ireland politics. Negotiators were also sparring over whether that would cover Northern Ireland or mainland Britain as well.
"The majority of people in Northern Ireland are looking for something quite different from what the DUP is looking for, and yet the DUP is given this platform as if it speaks for Northern Ireland".
As May prepared to update key Cabinet ministers on progress toward a deal, Ivan Rogers said that, more than two years after voting to leave the EU, Britain is "on fantasy island" about what kind of divorce agreement is possible. May's Conservative Party is also divided over how close an economic relationship to seek with the European Union after Brexit, leaving the prime minister in a precarious position.
"We are working not just with the domestic preparations that we need to do, but with the Belgians, the Dutch and the French, to make sure not just passengers going, as you say, on holiday but also goods can continue to flow".
"Nobody thinks we can sign off on all the detail [of a future trade agreement] by the end of the year".