Sammy Wilson said his party would never turn against the government to support Labour or the SNP because they had "nailed their colours to the EU mast".
The DUP's Brexit spokesman appeared on the breakfast show to discuss the news that Theresa May will bring her withdrawal agreement to the Commons today.
When asked by Julia Hartley-Brewer whether he or his party would ever switch allegiances, he said: "The SNP don't want us out at all and the Labour Party can't make it's mind up whether it wants us out or to have a second referendum.
"I don't think we're going to be rushing to support a bunch of remainers who have clearly nailed their colours to the EU mast."
However, despite the DUP's support for the Conservatives, Mr Wilson insisted he would not be voting to support the deal.
"There are better ways of securing the exit from the EU than a deal which ties our hands the way this one does," he said.