The South Cambridgeshire MP, who defected from the Conservatives in February to join The Independent Group, said she had "some sympathy" with no deal being an option because it offered a "clean Brexit".
She suggested that voters could be given a choice between any Brexit deal approved by parliament, remaining in the EU and leaving without an agreement.
Change UK is committed to campaigning for a fresh referendum on Brexit.
Asked how another vote would work, she told The House magazine: “There’s clearly a bit more knocking around to do in the House of Commons in terms of what the emerging article is… Perhaps we have another round of indicative votes. Whatever comes out of that we put to the British people in a referendum versus Remain.
“There’s a debate to be had around whether you have a three-stage voting process that includes a clean no-deal Brexit because for some people, they believe that is Brexit. There’s maybe some debate to be had around that.”
Pushed on whether she wanted no deal to be on the ballot paper, she added: “I have some sympathy for it. The Electoral Commission would have a view about how it might split the vote or whether it might artificially give advantage in one direction or the other. That’s the argument people say, ‘well, you’ll be splitting the vote if it’s the leaving deal or the no deal’. If that is the conclusion, then clearly, we can’t have that.
“But I feel like we should be offering no deal because to some people that is clean Brexit. But one thing I am without doubt 100 per cent clear on is that ‘Remain as we are’ has to be on the ballot paper because that’s what we’re comparing. We’re in it, versus whatever the brave new world might look like.”
Ms Allen also admitted that Change UK's process for vetting candidates for next month's European Parliament elections was "not good enough" after two candidates were forced to step down after having been found to have previously made offensive comments on social media. One had posted saying that "black women scare me" while another had made derogatory remarks about "Romanian pickpockets".
The Change UK interim leader said the party had employed a "professional top end vetting company" but that they had "missed a couple of things".
Asked how the row made her feel, she said: “Angry, disappointed. It’s unprofessional, it’s not good enough. But we’re not perfect, nobody’s perfect. In life, in any area of life, you accept you can’t do everything yourself. That’s why you pay other organisations or businesses to do things for you where they have the skills, recognising that you don’t."
Ms Allen said her party needed to focus on "the really important stuff", including welfare and education, rather than Brexit alone.
She said: "Brexit is a massive, massive issue, but it cannot be everything that we're about.
"I want to get onto the exciting stuff, I want to sort welfare out, I want to deal with education, I want to get some proper funding in my schools.
"I want to get onto all that other stuff, but Brexit, as it is with everything in life, is just stalling and stopping us from getting onto the really important stuff."
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