That would keep the UK in the EU for longer.
The party’s Brexit spokesman Sammy Wilson said if a deal went through, Britain would have lost its right to leave the EU.
He wrote for the Telegraph website: “Even if we are forced into a one-year extension, we at least would have a say on the things which affect us during that time and would have the right to unilaterally decide to leave at the end of that one-year period through the simple decision of not applying for a further extension.”
So far, the DUP has given no indication it will end its opposition to the deal.
Mr Wilson said: “Surely this is a better strategy than volunteering to be locked into the prison of the withdrawal deal with the cell door key in the pocket of Michel Barnier.”
The Democratic Unionists’ ten MPs prop up Mrs May’s minority government.
They want to avoid any proposals which would see Northern Ireland’s regulatory regime diverge from the rest of the UK.
They are staunchly opposed to the backstop insurance policy, which would prevent the imposition of a hard border on the island of Ireland by tying Northern Ireland to aspects of EU regulations affecting trade.
Mr Wilson said: “There are some colleagues who I admire greatly and who have stood firmly with us in defending Northern Ireland who now take the view that the withdrawal agreement, even though it is a rotten deal, is better than losing Brexit.
“To them I say that, if the deal goes through, we have lost our right to leave the EU.”
The DUP have urged Tory Brexiteers to continue to “stand firm” against the Prime Minister’s deal unless there were significant changes.
Indicative votes are due to be held in Westminster tomorrow.
On Thursday, a meaningful vote three has not been ruled out.