The Work and Pensions Secretary has said that there is a "plausible" argument for a second referendum if the Prime Minister's Brexit deal is rejected.
Amber Rudd suggested that she could see a situation where there might be a fresh vote if Theresa May fails to get her controversial deal for leaving the European Union through the Commons.
"I don't want a people's vote, or a referendum in general, but if Parliament absolutely failed to reach a consensus I could see there would be a plausible argument for it," she told ITV's Peston.
"But I think it is incumbent on MPs to find the centre ground in Parliament and to try to find where the majority is there. Because, quite frankly, I don't think the majority of people ... want to be asked again how to vote."
It appears to be the first time a cabinet minister has said there is a plausible argument for a second referendum.
Ms Rudd has previously suggested a Norway-plus model soft Brexit could be plausible if MPs were asked to back an alternative to Mrs May's deal.
She backed the idea of an indicative vote where MPs could reveal which options they would back if Mrs May's deal cannot get through.
"I quite like the idea of indicative votes because it would flush out where people's majority is, so people who hold on to the idea of one option or another would see there's no majority for that so they need to move to their next preference," she said.
"We would hopefully be able to find where the compromise and the consensus is for a majority of support."
Her comments come after Welsh First Minister Mark Drakeford told reporters in Downing Street that a second referendum would be "unavoidable" if no deal was agreed by MPs and there was not a general election.
"The Prime Minister should put her deal to the House of Commons and see what support she can mobilise for it and see whether there are any alternatives - a Norway-plus arrangement for example - that might have a better chance of responding to where the centre of gravity in the House of Commons may currently lie," he said.
"If the House of Commons is deadlocked we need a general election and a new House of Commons.
"If we are denied that, then it seems to me unavoidable that the decision would have to go back to the people."
