The BBC reported that several cabinet ministers have told it a no-deal Brexit could lead to a vote on Irish unification.
One senior minister said the prospect is "very real" and very much on the prime minister's mind.
A second cabinet minister warned the government risked "sleepwalking into a border poll".
And a third cabinet minister said there was an understanding in government that a vote on unification would be a "realistic possibility" if the UK exit the EU without a deal next month.
"If we are party to creating an environment of chaos, disruption and uncertainty - that could move the dial", the source told.
All three spoke to the BBC on condition of anonymity.