Labour Deputy Leader and Black Country MP Tom Watson has said it is "highly unlikely" his party would call for a second referendum on Brexit.
But he said the option hadn't been taken "off the table".
Mr Watson, MP for West Bromwich East, also mocked former Foreign Secretary Boris Johnson, who resigned in protest at Theresa May's Brexit policy - saying Boris would make a good contestant on Love Island.
Speaking to BBC Radio 4, he said: "It is conceivable that there is no majority position for any deal in the current arrangements in Parliament.
"So, even though we'd prefer a meaningful vote in Parliament, and I have said many, many times it's highly, highly, highly unlikely we will support a people's vote, and we have not called for it, we haven't taken that off the table because there are a rare set of circumstances where Parliament just can't make a decision on it, and in those circumstances you'd keep your options open.
"But ... it's highly, highly unlikely we'll go down that route."
He hit out at Boris Johnson, who was photographed signing his resignation letter.
Mr Watson said: "Look at that guy Boris Johnson, I mean, he's got a career ahead of him on 'Love Yourself Island', I think.
"He's the only politician in history who posed to sign his own resignation letter."
In the letter, Mr Johnson launched a scathing attack on Prime Minister Theresa May's Brexit policy, telling her: "The Brexit dream is dying".
And he said the UK was set to become a "colony" of the EU.
Mr Johnson said: "We are truly headed for the status of colony - and many will struggle to see the economic or political advantages of that particular arrangement."
But Mr Johnson received a boost - depending on how you look at it - when he was endorsed by US President Donald Trump, who arrives in the UK for a visit on Thursday.
Mr Trump said: "Boris Johnson is a friend of mine. He's been very, very supportive and very nice to me. Maybe I'll speak to him when I get over there."
However, Mr Trump said the UK was "in turmoil" and meeting US President Theresa May might be harder than meeting Russia's President Putin.
He said: "It's going to be an interesting time in the UK and an interesting time at Nato. We will work it out and all countries will be happy.
"So I have Nato, I have the UK - that's a situation with turmoil. And I have Putin. Frankly, Putin may be the easiest of all."
On his trip to Europe, he added: "It's going to be an interesting time in the UK and an interesting time at Nato. We will work it out and all countries will be happy.
"We do have a lot of allies. But we cannot be taken advantage of. We're being taken advantage of by the European Union. We spend 75% on Nato and frankly, it helps them more than it helps us."
