The meeting with Dutch Prime Minister Mark Rutte and Denmark's Lars Lokke aims to ensure Brexit negotiations do not stall on withdrawal talks, but move swiftly to discussions about the longer-term UK-EU relationship.
Kenny is also expected to highlight specific Irish concerns, including the future of the border and common travel area.
Meanwhile, further details have emerged of European Parliament President Antonio Tajani's meeting with UK Prime Minister Theresa May, taking place on Thursday.
A spokesperson for Tajani said, "The President will discuss the European Parliament's position on the withdrawal of the UK from the European Union and a resolution defining its guidelines for the negotiations."
This was passed by MEPs with an overwhelming majority on 5 April.
The motion backs a number of positions taken by EU leaders, including the need for a "phased approach" to negotiations.
This would require progress on the terms of Britain's withdrawal, including settling financial commitments, before talks on a future trading relationship can start.
It also backs the call for transparency in the talks, and for the UK to be considered liable for financial commitments that apply after it leaves the EU.
After meeting May, Tajani will hold a press conference at the European Parliament information office in London.
Later, he will have an exchange of views with NGOs that have, as one of their main concerns, the rights of EU citizens in the UK in the Brexit negotiations.
Elsewhere, the British government's Brexit department says that the future location of the two EU agencies based in London will be a matter for Brexit negotiations even though EU officials said there was no doubt they would be moved.
London is home to both the European Medicines Agency (EMA) and the European Banking Authority (EBA), and last month the EU's draft plan for negotiations said arrangements should be made to transfer them to a state staying in the EU.