David Lidington, who is leading the talks with Labour on subjects such as environmental standards, workers rights and the security relationship with the European Union, said the discussions were going to continue next week but that they wouldn't last months.
However, the European Union has insisted the terms of the UK's withdrawal, rejected three times by MPs, can not be renegotiated - but there is scope to strengthen the political declaration, a document setting out the parameters of the UK's future relations with the European Union, ahead of the new Brexit deadline of 31 October.
Lidington told the BBC compromise talks with Labour would continue, with both sides seeking agreement over a plan for Brexit that could win parliament's approval.
However, now in talks between the two parties, the issue of a customs union is thought to be creating a sticking point.
Central among the issues for the talks is whether the government is prepared to give ground to Labour on a future customs union with the European Union - something ministers oppose, but which is a key plank of Labour's Brexit proposal.
Such a move would limit the UK's ability to strike trade deals with non-EU countries, a central aim of Brexiteers.
Lidington said the government believed it was possible to gain the benefits of a customs union without losing the power to strike independent trade deals.
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A Labour source said: 'Our MEPs are all pro-Brussels and do not want to fight alongside anti-Brussels Labour candidates because they say it will show the leadership is facing both ways.
Asked about the possibility of a confirmatory referendum, he said the UK Government's position is "very clear".
Labour leader Jeremy Corbyn is coming under increasing pressure from his own party members to fully commit the party's support to a confirmatory referendum.
He continued that if this happened, then the Government would "stand ready to implement what Parliament decides".
May has come under fire from MPs including former leader Iain Duncan Smith following her decision to agree an extension that would result in the United Kingdom taking part in European elections next month.
"A second referendum still went down to defeat and I just question whether there is a majority for it in the House of Commons".
Removing May and replacing her with a new leader would "not change the arithmetic" in parliament, he explained.