The Government is keen to move on to talks about the UK’s future relations with the EU beyond the three areas already discussed.
Theresa May’s spokeswoman suggested that negotiators are ready to discuss elements of the UK’s ties other than the Northern Ireland border, the rights of EU citizens and the UK’s Brexit bill.
The spokeswoman said: “We are ready to intensify negotiations. Nothing has been formally agreed, but that is something that we can discuss.
“Typically in negotiations as time goes on you see the pace pick up.”
Currently, the negotiating only takes place for one week each month in Brussels. There reports the UK wants to move to continuous talks.
On Friday, the EU’s chief negotiator, Michel Barnier, said at the end of the third round of talks in Brussels that there had been “no decisive progress” on key issues.
On Monday, after a meeting with the Republic’s foreign minister Simon Coveney, Mr Barnier restated his aim to resolve the questions posed by Brexit for the Ireland-Northern Ireland border ahead of trade talks.
The EU has previously stated it does not want to discuss future trade-relations until issues over the border, the rights of EU citizens living in the UK and how much the UK should pay the EU have been resolved.
Despite this, the PM’s spokeswoman said the Government will on Wednesday publish a position paper on post-Brexit science and innovation relations with the bloc.
“Currently we are talking with the EU about withdrawal,” she said. “We want to be talking about withdrawal and the future partnership.
“We are not at the stage in negotiations where we are talking about the (Brexit bill) figure. We will seek a fair settlement of our rights and obligations as a departing member state, but we are not at that stage yet.”
On Sunday, Brexit Secretary David Davis accused the EU of playing “time against money” by trying to exert pressure on the UK to agree a divorce bill.
It was reported over the weekend that Mr Barnier said he wanted to get as much money out of the UK as possible.
Speaking at a conference in Italy, Mr Barnier claimed he needed to educate the UK about the price it would pay for leaving the EU.
On Twitter on Monday however, the EU negotiator claimed he had told delegates that Brexit was an “occasion to explain single market benefits in all countries, including my own”, adding: “We do not want to ‘educate’ or ‘teach lessons’.”
Former UKIP leader Nigel Farage called on the Government not to waste 18 months negotiating with the EU only to end up with no deal.
He told Sky News that the Government should go directly to leaders of the other 27 EU countries and large firms and bypass Mr Barnier and European Commission President Jean-Claude Juncker.
Mr Farage’s comments came ahead of a major summit of EU leaders next month, at which Brexit is likely to be high on the agenda.
Mr Farage said: “We’ve got to appeal above the heads of the negotiators. We’ve got to go straight to national governments and indeed European companies to say a trade deal is in everyone’s interest.”
Preparations for the next round of talks come as Downing Street called for unity among its MPs ahead of a debate on the Government’s flagship Brexit legislation.
The EU Withdrawal Bill will repeal the law that allowed the UK to join the European Economic Community in the 1970s and switch 40 years worth of EU law into domestic law.