Speaking to Reuters on the sidelines of a trade fair in Shanghai, Fox said it was more important to get the right agreement than the quickest agreement.
British trade minister Liam Fox said on Tuesday it was "impossible" to say whether a Brexit deal could be reached with the European Union this month or next, but that Britain wanted an agreement, and a deal is better than no deal.
Mrs May proposed to keep the entire United Kingdom tied to the EU's Customs Union as a compromise, while Brussels was pressing for Northern Ireland to be subject to Single Market regulations as well.
Britain is confident that it will "imminently" reach a deal with the European Union on its post-Brexit financial services trade with the bloc, British financial services minister John Glen said Monday.
According to the Telegraph, May has included Attorney General Geoffrey Cox, the government's chief legal advisor, in her special Brexit Cabinet after ministers said they wouldn't sign off on a deal without his advice.
On Friday Mr Lidington and Brexit Secretary Dominic Raab visited Ireland and Northern Ireland respectively for talks with senior political figures as the deadline for securing a Brexit deal moved closer.
The plan sees the whole of Britain remaining in the EU customs union - not just Northern Ireland.
This comes after backbenchers are pressuring May to ensure there is a time limit on the backstop.
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"Goodness, we have been here on a number of occasions and I think we are close to a deal that will work for Northern Ireland, that is what we want", said Foster, whose party threatened to pull the plug on the government less than a month ago if the Brexit deal involved a border in the Irish sea.
Downing Street claimed the report about the deal is "all speculation".
However, if these Brexiteers are not convinced that the customs union is only a temporary measure they would nearly certainly rebel. The prime minister has been clear that we are making good progress on the future relationship and 95 percent of the withdrawal agreement is now settled.
"Anything that weakens or softens the Irish Government's position as to the baseline protections that we need is something to be avoided", she said.
"This is the backstop", he added, saying the United Kingdom had agreed that it would apply "unless and until" a close future relationship eliminated any need for Border infrastructure and checks.
"Looks like we're heading for no deal", he tweeted.
Sinn Fein president Mary Lou McDonald has urged the Irish premier to stand firm over a proposed backstop plan to prevent a hard border in Ireland after Brexit.