On the issue of "regulatory alignment" - the phrase around which the Irish Brexit deal is anchored - Mr Varadkar said this did not mean Northern Ireland and the Republic would have the exact same rules.
Mr Varadkar and Ms May spoke earlier on the phone, and the Taoiseach said he would look at positions proposed by the UK.
"We didn't discuss the detail of any new language".
After talks in Dublin, Irish Taoiseach Leo Varadkar and Dutch PM Mark Rutte made clear the European Union would not compromise and allow the Irish border to be kicked down the road to phase two of the talks, even under threat of Britain crashing out with no deal or divorce negotiations dragging on to 2018.
Pressure is growing on Mrs May to get leaders at the December 14 European Council summit to declare sufficient progress has been made on divorce issues so trade talks can begin, with business chiefs warning companies will activate contingency plans that will cost Britain jobs if there is further delay.
He said things have to be sorted this week, adding: "Our week includes Sunday".
Speaking on BBC Radio 4's Today programme, the transport secretary said people had misunderstood the key term "regulatory alignment" which has been the focus of the debate.
With Brexit, the United Kingdom is leaving the EU's customs union - but Mr Grayling said this did not mean there would need to be a physical border with people carrying out border checks. They could then approve those guidelines at European Union summits due in February, or failing that in March, sources said.
Meanwhile, the Prime Minister was facing a growing civil war in her own party over her approach to the negotiations, as pro and anti-EU Tories traded insults.
DUP chief whip Jeffrey Donaldson said: "Discussions are ongoing".
But they hit out at what they say are attempts by some in their party to paint a no-deal scenario in which the United Kingdom failed to agree a trade agreement as "some status quo which the United Kingdom simply opts to adopt".
The EU's chief Brexit negotiator Michel Barnier has cautioned that the talks on the United Kingdom leaving the bloc will not shift to the next stage if London fails to arrive at a consensus on a text about the relevant deal in the next 48 hours.
Scotland's nationalist leader showed little patience, accusing the British government of being "totally and utterly incompetent" on Brexit. "That means jobs leaving the United Kingdom - in most cases irreversibly".