Coming a week ahead of a crunch European Council meeting of leaders in Brussels, the visit is a clear demonstration of the EU's solidarity with Ireland's position.
Rules governing the border post-Brexit represent one of the most vexed issues facing the negotiators in Brussels.
Ministers face another showdown with their critics in the Commons on Wednesday over giving MPs a "meaningful vote" on the final Brexit deal.
The withdrawal agreement must contain a fully operational backstop solution for Ireland and Northern Ireland.
"It's as tricky as it sounds, so we are grateful for the diligence and understanding shown by the Commission's lead negotiator, Michel Barnier, in his conduct of these very hard negotiations for the European Union".
Continuing, McGuinness said: "I look forward to meeting Michel Barnier and Jean-Claude Juncker in Dublin tomorrow".
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"We wanted to make it clear again and again that Ireland is not alone, we have Ireland backed by 26 members states and by the Commission and that will not change", Juncker said ahead of an address to both houses of Ireland's parliament.
Mrs May faces an European Union summit on 28 June, at which both sides were hoping to demonstrate progress in the Brexit negotiations.
Britain and the European Union want to keep a free flow of people and goods over the border without returning to checkpoints, symbols of the three decades of violence in Northern Ireland that was largely ended by a 1998 peace deal.
"I'm strongly against any temptation to try and isolate Ireland and not to conclude a deal on Ireland".
Juncker made the comments in a joint press conference with Irish Prime Minister Leo Varadkar at the start of a two day visit to Dublin to discuss Brexit issues. I expect that they will express their strong support for Ireland in the Brexit negotiations.
"We call on the UK Government in its forthcoming white paper to commit to staying inside the single market and customs union recognising that this will require continued alignment with the EU regulatory environment".
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"Serious divergences remain, however, on the protocol on Ireland/Northern Ireland".
Later, Mr Juncker received an honorary degree from the National University of Ireland.
Across Great Britain, 62 per cent of respondents said Brexit negotiations were proceeding too slowly, with 30 per cent blaming the delays on "politicians in Britain who want a soft Brexit or to stop Brexit altogether".
Talks between the United Kingdom and the European Union have focused on the future arrangements on the Irish border.
On Friday the Commission President will meet Irish President Michael D Higgins and visit the home of the Gaelic Athletic Association (GAA), Croke Park, and the GAA museum. "It remains our intention to achieve a close economic partnership that does not require the backstop to be in operation".
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