The Times reported that such a border is the EU's preferred option, after seeing a letter May sent to the Democratic Unionist Party (DUP) saying she would not let this "come into force".
"I must caution that there is high level of uncertainty when you are making any projections in relation to Brexit", he said.
He said the two sides were discussing how to avoid a hard border between Ireland and Northern Ireland.
Downing Street reiterated the PM's own commitment to avoiding a hard border.
But the DUP has interpreted the wording of her letter to mean that the EU's proposal - known as the "backstop to the backstop" - will be contained in the Brexit divorce deal despite Mrs May's insistence it will never come into effect.
She added that any backstop could not leave Northern Ireland aligned to specific sectoral European Union market regulations.
The DUP, who are critical in helping the Tory minority government stay in power see this leaked letter as part of May's preparatory work, before a likely showdown with the party concerning checks in British ports or factories in Northern Ireland or Britain.
The party's Westminster leader, Mr Dodds, warned on Sky News: "I think the Prime Minister will hopefully realise what can be got through parliament and what can't".
Less than five months before Britain is due to leave the European Union on March 29, negotiators are still haggling over a backup plan for the land border between British-ruled Northern Ireland and European Union member Ireland should they fail to clinch a deal.
Ireland's Taoiseach Leo Varadkar, Mrs May's effective deputy prime minister David Lidington, and Northern Ireland Secretary Karen Bradley were attending a summit in the Isle of Man.
Speaking at the British-Irish Council summit in the Isle of Man today, Mr Varadkar said he was hopeful the United Kingdom could strike a deal with Brussels before the end of the year despite continuing concerns over the future of the Irish border.
We caught up him today to ascertain what he thinks will be the likely animal feed industry exposure to Brexit, both in the context of cross-border trade on the island of Ireland and the flow of feed trade between the United Kingdom and Ireland more generally.
"And we'll do our best to work through it and make sure we get the best outcome for our citizens".
"There is no clean break here, Brexit is going to go on for a very long time".