The Irish Prime Minister thinks it will be 'impossible' for the UK to hit its Brexit deadline
UK Prime Minister Theresa May plans to trigger Article 50 of the Lisbon Treaty in March next year, at which point the government has two years to agree the terms of the country's departure.
But Kenny - who is known as the Taoiseach in EU member nation Ireland - said there is a "growing feeling" in Europe that the Brexit deadline of spring 2019 is unrealistic.
"I think it will be impossible to do the negotiations within the contemplated two-year period," he told Sky News on Friday. "That's why I think there's a growing feeling in Europe that there should be a transition period, and that the transition period will be longer than those two years - I think it will be."
Kenny pointed out that the negotiations are unprecedented, given that no country has left the EU in 50 years. "It's more detailed and [there will be more] unforeseen issues than people might have imagined, so I would expect to see it take place, but that there be a transition period and then a new relationship founded," he added.
May has previously hinted that the Brexit timetable may be longer than two years. She told Parliament in October that the process would take "two years and more." She did not elaborate further.
Kenny also alluded to division in May's top ministerial team over the issue of Brexit. He has "not yet" seen a coherent Brexit plan, he said, adding that there had been "different statements made by different people."
The Irish PM was speaking to Sky News political editor Faisal Islam at the British Irish Council near Cardiff in Wales. May did not attend the Brexit-themed meeting - a decision that was questioned by other leaders at the gathering.
Martin McGuinness, the deputy First Minister of Northern Ireland, said: "She is a new British Prime Minister, this was her first opportunity to attend the meeting of the British Irish Council and to meet with the devolved institutions and the Crown dependencies and I think it was a missed opportunity on her behalf."