BBC political editor Laura Kuenssberg said it was understood that the EU was prepared to accept the idea of the whole of the United Kingdom remaining in the customs union if a trade deal can not be done during the so-called "transition period", which is due to end in December 2020.
In addition, Northern Ireland would remain under large parts of single market regulations, requiring enhanced checks on products arriving from Britain, particularly agricultural goods.
May set out in June proposals for a "temporary customs arrangement" to ensure that the border remains open in the case that no broader EU/UK trade agreement has been finalised.
Michel Barnier said that up to 85 percent of the work is done on the deal for the U.K's departure and post-Brexit relationship with the European Union, but the issue of ensuring a transparent border on the island of Ireland remains to be addressed.
She said: "I am completely supportive of the prime minister".
"The Prime Minister is a unionist".
Downing Street also announced a further 29 no-deal notices would be published on Friday afternoon, setting out what businesses and consumers should do in the event of there being no agreement by 29 March 2019.
The DUP is propping up Mrs May's minority government and on Wednesday they threatened to vote down the budget and move to topple the government if the Prime Minister breaches their Brexit "red lines".
Air India flight hits airport wall before take-off
Ganesh Babu who has flying experience on the B 737 aircraft of 3600 hours including about 500 hours as Commander. The pilot however continued to operate the aeroplane saying the systems were operatinf normally.
She repeated that Britain wanted a new trade deal by the end of December 2021 at the latest.
Meanwhile, Chancellor Philip Hammond became the first senior Government figure to suggest that the backstop - created to keep the border between Northern Ireland and the Republic open in the case that no broader EU/UK trade deal is finalised - will "probably" have to come into effect for a period.
Intense talks will continue over the weekend as both sides attempt to make a Brexit deal possible when leaders gather in Brussels next week.
Brexit negotiations with the European Union have accelerated and become more positive over the past week, though significant hurdles remain, finance minister Philip Hammond said.
"She will not have DUP support regardless of whether the government tries to bribe, bully or browbeat us into accepting it", Wilson also said.
On Wednesday, EU chief negotiator Michel Barnier said there would have to be checks on goods travelling to Northern Ireland from the rest of the United Kingdom, because they would effectively be arriving in the EU's single market if there was no hard border with the Republic of Ireland.
He hit out the "not so subliminal bullying" by Tories opposing her strategy in the middle of negotiations and also criticised International Development Secretary Penny Mordaunt, who declined to give the PM's plan her explicit backing when asked earlier this week.
But the European Union is mounting resistance to any specific time limit being included in the text of the UK's Withdrawal Agreement, while Leave-backing ministers are understood to be insistent that the end of the arrangement should be more precisely defined than the vague term "temporary".