The Taoiseach claims a border poll would be easily defeated and would be 'divisive'.
There have been widespread calls for Leo Varadkar to set up a citizens assembly to discuss the prospect of a united Ireland.
It follows the recent general election results in the North, which saw Unionists lose their majority for the first time.
But the Taoiseach claims there still isn't enough support for a border poll to succeed because parties that support a united Ireland also don't have a majority, with their backing at around 40%.
Sinn Féin has increased call for a border poll in the wake of the UK election.
They also supported the findings of a poll by The London Independent in September which showed widespread UK support for a referendum on the border.
At the time of those findings being published, Sinn Féin leader, Mary Lou McDonald said 'change is coming' while adding that the government and the Taoiseach can't bury their heads in the sand over the issue.