The Prime Minister will meet the European Commission President and Mr Barnier at Downing Street in what is being described by European officials as a “flying visit” on Wednesday.
It comes ahead of the crucial summit this weekend at which European leaders will formally adopt draft Brexit negotiating guidelines, that remain largely unchanged since they were first proposed in March.
The visit to the UK by the two top EU figures will also be the first time the Prime Minister meets Mr Juncker and his head negotiator since setting the UK on course for a general election to be fought along Brexit battle lines.
The Independent understands Mr Juncker and Mr Barnier will not do a press conference with the PM when they come to No 10, but will only hold private talks with Ms May during a closed-meeting in the evening.
An EU source told The Independent: “At the meeting they will discuss the guidelines ahead of the summit.
“But the purpose will also be to present Mr Barnier in person as the head man to be dealt with in Brexit negotiations.”
Saturday’s special Brexit summit of EU leaders, excluding Ms May, will be when they formally approve the negotiating guidelines that were put forward by European Council President at the end of last month.
The inclusion of an article in the guidelines, which effectively gives Spain a veto over any deal affecting the status of Gibraltar, caused consternation among some in the UK – in particular ex-Tory leader Michael Howard, who said Ms May would go to war with Spain to uphold the territory’s British status.
On Monday in Brussels, however, a preparatory meeting of sherpas agreed that the guidelines would be put to EU leaders without any substantial changes to the proposed approach put forward by Mr Tusk.
Sources said discussions were “consensual and resulted in only a few technical adjustments”.
Another EU insider said: “Gibraltar is still in there. The exclusion of sectoral deals on the single market is in there. It is largely unchanged.”
After the EU 27 formally adopt the Brexit guidelines, officials at the Commission will begin to flesh them out, with an eye on shaping more intricate and detailed negotiating “directives” to be approved at the end of May ahead of formal Brexit talks, which will then start after the UK’s general election.
Ms May is widely expected to make several Brexit-based pledges as part of her bid to secure a more workable majority in the House of Commons, including guarantees that she will end free movement, end the jurisdiction of the European Court in the UK and pull out of the EU single market.
But the solidity of each pledge is already under question – with Ms May and Brexit Secretary David Davis both already signalling, for example, that free movement may continue for a period after the UK leaves the EU.
The guidelines to be approved by EU leaders on Saturday also rule out the kind of sector-by-sector access to the single market that Ms May’s allies have suggested could provide the basis for an agreement.
Meanwhile, her promise to end the European Court’s jurisdiction in the UK hit a block after it emerged the EU will push for the body’s power in the UK to be upheld after Brexit, in particular when it comes to preserving EU citizens’ rights in Britain.