The Taoiseach is likely to seek an early meeting with incoming British prime minister Theresa May, who is due to take office in Downing Street on Wednesday evening.
Irish Government sources say Ms May is reasonably well known to them, as there is a high degree of co-operation between the two governments on security and justice issues.
“She managed to survive in the home office for seven years. So we would obviously respect that,” said one official. The home office is regarded as the most difficult British department of state.
"She's very easy to work with, very pragmatic, very clear," said Minister for Justice Frances Fitzgerald tonight. "We worked closely together on justice and home affairs issues, and she is familiar with Northern Ireland issues."
Among the contenders that emerged for the Tory leadership – and therefore for the office of prime minister – Ms May was regarded by the Irish Government as the best option.
Some of the most important issues for Ireland come under the home office and Irish officials speak highly of her key civil servants - permanent secretary Mark Sedwill and his deputy Olly Robbins.
Mr Robbins has been appointed head of the overall Brexit team across the British government. A group of British home office officials visited Dublin to discuss Brexit last week.
Position reversed
The Government was also happy when Ms May recently reversed an earlier position in favour of taking Britain out of the European Convention on Human Rights.
Dublin has previously warned the UK that taking Northern Ireland out of the ECHR would be a breach of the Belfast Agreement.
Taoiseach Enda Kenny enjoyed a warm relationship with outgoing prime minister David Cameron, which officials will seek to replicate with Ms May, though sources say she tends to be "businesslike" and "pragmatic" in meetings.
