The Taoiseach has been in contact with the British Prime Minister today as Brexit talks intensify.
Mr Varadkar spoke with Boris Johnson, with the two leaders planning to meet again at the UN summits in New York next week.
The UK's Chancellor has also met with Finance Minister Paschal Donohoe today.
Sajid Javid has said it is essential the UK and Ireland maintain their positive relationship after Brexit.
“Whatever happens next year regardless of Brexit, it is essential that not only we maintain the strength of our relationship between our two great countries but we find ways to enhance that,” said Mr Javid.
Mr Javid was in Dublin today to meet Mr Donohoe to discuss Brexit and the importance of maintaining a strong economic relationship as the UK leaves the EU.
This is the third time the men have met in the eight weeks since the Chancellor started his position.
In a statement, the Department of Finance said this reflects the importance of economic relations between Ireland and the United Kingdom.
Speaking to reporters after the meeting, Mr Donohoe said: “We have always said on many occasions that in any circumstance, the relationship between both our countries will be so important and the close working relationship between the Treasury, the Irish Department of Finance will be essential.”
This bilateral meeting takes place six weeks ahead of the Brexit deadline on October 31.
It follows on from a meeting held between DUP leader Arlene Foster and Mr Varadkar in Dublin on Wednesday night where they discussed Brexit and ongoing efforts to restore the Northern Ireland Assembly.
A number of members of the House of Commons Committee on Exiting the European Union, including committee chairman and Labour MP Hilary Benn, are also visiting Ireland today.
- Press Association, with additional reporting by Digital Desk staff