The Taoiseach is due to speak to the British Prime Minister by phone next week.
Boris Johnson has already accepted an invitation to meet with Leo Varadkar in person; however, that meeting is unlikely to happen until September.
The two men are now due to speak over the phone before Mr Johnson travels to Paris for a G7 meeting of the world’s economic powers.
They are due to speak about Brexit, the political situation in Northern Ireland and bilateral relations.
Mr Johnson has insisted he remains determined to strike a new Brexit deal with the EU, while also preparing to leave without one on October 31st.
The EU has not moved from its position that the Brexit Withdrawal Agreement, including the backstop, is not open for renegotiation.
In the UK meanwhile, MPs are continuing to discuss ways to prevent the UK crashing out.
The opposition Labour Party leader Jeremy Corbyn has put forward a plan to call a no-confidence motion in Mr Johnson as soon as “we can be confident of success.”
If that vote passed, he would ask other to supports "strictly time-limited" government with him as caretaker prime minister.
He would then quickly call a general election while seeking an extension to Article 50.
He said Labour would then campaign for a second Brexit referendum - which would include a 'remain' option.
Interim Prime Minister
His plan was quickly rejected by the Liberal Democrats and pro-Remain Conservatives, who have said they could not support him as prime minister for any length of time.
Negotiations are continuing with other names put forward to lead the unity Government including Ken Clarke and Harriet Harman.