His hint at a climbdown comes amid signals Brussels could reject her vision for the UK's long-term relationship.
Mrs May is hoping to get a post-Brexit transition period signed off at the European Council summit of EU leaders on March 22-23, clearing the way for exploratory talks on trade.
The Tory grandee dismissed the Prime Minister's Mansion House speech on Friday, saying it offered "the wrong answers at the wrong time for the wrong reasons".
Mrs May's out of hand rejection of the document has caused concern in Ireland and raised eyebrows in Europe.
The proposal, he said, was a "starting point" for talks not a solution.
But, underlining the challenge May faces, Ireland's foreign minister, Simon Coveney, said on Sunday she still had to spell out her approach to the Irish border.
"What we want is not so much principles and aspirations and red lines", Mr Varadkar said.
Mrs May's speech was meant to conclude a mini-series by ministers.
But although May did not dispel the impression of "cherry-picking" European Union benefits or of trying to have Britain's cake and eat it, European Union officials working on the negotiations behind the scenes welcomed what one called her "positive directional language". She added: "It was a vision that was ambitious but was also practically based and therefore a credible vision".
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"More is needed to lift the fog of uncertainty and we welcome the PM's call to "get on with it".
"There are two areas which have never been covered in a Free Trade Agreement in any meaningful way before - broadcasting and, despite the EU's own best efforts in the Transatlantic Trade and Investment Partnership, financial services". The Union is deeply sceptical of suggestions to let Britain regulate itself, free of EU supervision, while retaining anything like its current access to EU markets, notably in many services. But she also wants the European Union to give her a deal on the City's access to the European Union if she in return maintains the same level of regulations as the continent. But it was not a vote for a distant relationship with our neighbours. "But we should only allow new barriers to be introduced where absolutely necessary".
"Well, you see this is the mistake that I think is made in Britain all the time", Coveney responded, "when somebody definitively says that something "will be the case" from the British government, people assume that that is the negotiated outcome - of course it's not".
"Third, it must protect people's jobs and security".
Speaking at Mansfield College, Oxford, he said the lack of clarity as to how she would achieve a deal with Brussels would do nothing to reassure businesses considering whether to invest in the UK.
"Now we do have an opening negotiating position". A country that celebrates our history and diversity, confident of our place in the world; that meets its obligations to our near neighbours and far off friends, and is proud to stand up for its values.
"What the prime minister needs to lay out is some concrete proposals", he said.
"I welcome the Prime Minister's clear commitment that she will not countenance any new border being created in the Irish Sea between Northern Ireland and the rest of the United Kingdom".
Additional reporting from IRN.