"This is not a meeting about Brexit and the Prime Minister is not going to seek to turn it into one", one official said.
May has been trying to win legal concessions to the deal, which Labour and many lawmakers in her own Conservative Party voted against in a parliamentary vote in late January.
The Labour leader emerged from a meeting at the European Commission headquarters in Brussels and said that his proposals were the only way forward to prevent Britain crashing out of the EU next month.
The post, which refers to comments she made just before the EU referendum vote, reads: "I believe it is clearly in our national interest to remain a member of the European Union".
"I don't think it's the mechanism that matters, it's the objective", he told the BBC's Andrew Marr. We recognise that a no-deal Brexit would be a very bad outcome for the United Kingdom and we are doing everything we can to avoid that.
"The simplest way to get legally binding changes on the backstop is to reopen the Withdrawal Agreement".
It's just over a month before the United Kingdom is set to leave the European Union on March 29, and the risk of a no deal exit is rising with every day that passes.
May and the other 27 European Union leaders approved a Brexit withdrawal agreement at a summit on November 25 a year ago, but the British parliament voted against it overwhelmingly on January 15. "I'm losing my time with this Brexit", he said.
But unless the United Kingdom can finalise a Withdrawal Agreement by March 29 allowing Britain to continue participating in European Union trade deals during a 21-month transition period, it will enjoy the benefits of the Japanese agreement for just 57 days.
It comes as the UK's Brexit Secretary Stephen Barclay and British Attorney General Geoffrey Cox return to Brussels for further talks with the EU's chief Brexit negotiator Michel Barnier.
Outlining the steps that should be taken ahead of 29 March, the date the United Kingdom is set to leave the EU, Slattery said: "If you haven't sorted these issues before Brexit day your business will be in serious difficulty".
Earlier, President of the European Commission Jean-Claude Juncker said he was "not very optimistic" about Britain's chances of leaving the EU with a deal, also warning that any failure to agree an orderly Brexit deal will be economically costly. He told Today: "We are determined to get a deal".
Mr Hammond said the PM's ability to put her deal to another "meaningful vote" ahead of the next Commons showdown will "depend on (the) progress that is made over the next few days".
"This would be better than a divorce without agreement", he said.
Foreign Secretary Jeremy Hunt said the key to getting a deal approved by MPs was securing changes that would allow Mr Cox to alter his legal advice that the United Kingdom could potentially be trapped in the backstop indefinitely.
The backstop would see the United Kingdom choose between two options if trade talks with the EU fail to produce a deal after March 29, with the first being to leave Northern Ireland in a de facto no man's land where it remains a part of the United Kingdom but subject to the separate customs union and single market regulatory regime of the EU.
The statement from Juncker and May said they discussed possible "alternative arrangements" and changes to an accompanying political declaration as potential options.