The goal is to hammer out a new agreement that doesn't include an Irish border backstop, the mechanism to ensure that there will be no hard border between the Irish Republic and Northern Ireland if the sides failed to agree on all the terms of their relationship by the end of the Brexit transition period.
Under the backstop, the United Kingdom would remain in a customs union with the EU in the absence of a trade deal, and Northern Ireland would stay aligned to some EU rules.
The EU insists that the deal "remains the best and only way to ensure an orderly withdrawal", but with the clock running down until the March 29 exit date the risks of a no-deal Brexit for both Britain and the bloc are coming into sharp focus.
Writing in the Sunday Telegraph, the prime minister said she would return to Brussels with a "fresh mandate, new ideas and a renewed determination".
In an article for the Sunday Times, Simon Coveney, the Deputy Prime Minister of Ireland, wrote: "The EU will not renegotiate the withdrawal agreement and there will be no withdrawal agreement without the backstop".
Both the Irish government and the European Union have been adamant that the Withdrawal Agreement - including the backstop top avoid a hard border - won't be renegotiated.
Late last month, the MPs voted in favour of an amendment that was tabled by Sir Graham Brady to look for "alternative arrangements" to the Irish backstop after the MPs turned down the Brexit deal of the Prime Minister by historic margins last January.
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Pereira hit a shot from the edge of the box straight at De Gea, who gathered as United went into the break with a 1-0 advantage. He's been top scorer but he's been developing. "For me, it's about how you work with the players and work with the club".
"Nor do I have time for those who believe the verdict passed by the British people in 2016 should be overturned before it is even implemented", she added, referring to the rump of MPs calling for a second referendum.
The move, first reported on Saturday by Sky News, was confirmed by the company in a letter to workers Sunday.
May is due to report back to parliament on her negotiations with the European Union on 13 February, a few weeks after she secured MPs' support to go back to Brussels.
"I'm determined to deliver Brexit, and determined to deliver on time - on March 29, 2019", she wrote.
May said she is determined to deliver Brexit on time.
Leo Varadkar, president of the European Commission Jean-Claude Juncker and European Council president Donald Tusk will meet on Wednesday for a number of Brexit-related meetings.
Labour leader Jeremy Corbyn's party has fallen 6% since the Commons votes on Brexit took place, he has fallen from 40% down to 34% and public approval of Corbyn has dropped to 16% from 18%.