
The taoiseach also cautioned Europe against “losing the plot” over the UK’s decision to leave the EU.
In unscripted remarks before a conference in Dublin on the impact of Brexit on Ireland, Mr Kenny said the prime minister had indicated she will trigger Article 50 – the mechanism for leaving – before the end of March.
“That doesn’t mean it mightn’t be triggered in December ... or January, or February,” he added.
Mr Kenny suggested some European leaders would become very hostile to Britain.
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“The other side of this argument may well get quite vicious after a while, because there are those around the European table who take a very poor view of the fact that Britain decided to leave,” he said.
“That argument, I think, will be fought very toughly, in a really difficult negotiating sense.”
The issue of access to the single market being wedded to freedom of movement would be critical, he suggested.
Europe also has to decide for itself where it wants to be in the years ahead, he added.
“If it becomes obsessed with what the UK might or might not get, then Europe itself loses the plot,” he told the the All-Island Civic Dialogue, a specially convened forum of politicians, business leaders, community representatives and others from both sides of the border.
Northern Ireland’s main unionist parties, the power-sharing DUP and the UUP, both snubbed the talks.
Earlier, Mr Kenny told the gathering people will be able to travel freely between the UK and Ireland after Brexit.
The taoiseach said he has agreed with Mrs May that the “benefits of the Common Travel Area” between both countries should be preserved.
The deal, which dates back to the 1920s, secures freedom to travel between Britain and Ireland.
“I have agreed with the prime minister that there will be no return to the borders of the past,” he said. “Therefore, the retention of an open border is critical.”