The DUP could consider backing a Norway-style deal for Brexit as a way to prevent Northern Ireland being treated differently to the rest of the UK, Arlene Foster has said, stressing there is no way her party can back Theresa May’s plan as it stands.

Speaking immediately after EU leaders gave their formal backing to the proposed deal, Foster was adamant that the party she leads, which supports May in government, could never back the arrangement.

Asked on BBC One’s The Andrew Marr Show if there were any circumstances in which the DUP’s 10 MPs could vote for the deal, Foster replied: “No, there aren’t.”

She declined to say whether her party would remove its confidence and supply arrangement keeping May in power if the Brexit deal was passed by the Commons, saying only that she would “review” the issue in this case.

“We will have to see what happens at this time,” she said.

But Foster said it seemed very unlikely the plan would pass: “As far as I can see there doesn’t seem to be a great deal of enthusiasm in the House of Commons for this deal, quite the contrary. So let’s wait until we get to that vote. I don’t see any circumstances at present where that vote will be a vote to go ahead in Theresa May’s favour.”

The DUP’s main objection to the plan is the so-called backstop arrangement, the insurance policy insisted on by the EU to avoid a hard Irish border if no suitable permanent arrangement is found by the time the transition period ends, which would keep Northern Ireland aligned with Brussels regulations.

May has argued that there is no plan for this to happen, as the deal would be done in time. But Foster said this made no sense.

“It’s a legally binding text. You can’t have it both ways – you can’t say it’s not going to happen so don’t worry, and then on the other hand sell it as the best of both worlds,” she said. “There’s been an inherent contradiction with that argument.”

There was, Foster added, “the time now to look for a third way, a different and better way”.

According to the Sunday Times, the DUP has been discussing alternative plans with remain-minded cabinet ministers, including Philip Hammond, David Lidington and Amber Rudd.

Asked whether the party had been talking to ministers about the idea of a deal based on a model such as Norway’s, in which the UK would join the European Economic Area (EEA) and thus stay aligned to the single market, Foster did not dismiss this.

“Well, there are conversations going on right across government,” she said. “I don’t think that will surprise you. We’re talking to everybody across government. We’re talking to people in the remain side, we’re talking to Brexiteers, we’re talking to everyone, as I think you would expect us to do.”

Asked if the DUP could live with an EEA-type arrangement, Foster said: “We’ve always been very keen to give the government space to negotiate a deal in terms of Brexit. That’s the way we’ve always operated. But the one thing that we could not have was a difference between us and the rest of the UK in terms of international trade, in terms of customs and in terms of regulation.”

Pressed again, Foster said: “I’m not going to be prescriptive with the government. What I am saying to the government is: this deal, this current deal, does not allow us to take back control, certainly not in terms of Northern Ireland – we stay within the European Union structure and we will have no say on those rules. We will have a democratic deficit. We will have to take the rules with no way of influencing those.”