Sir Vince Cable has said there is a "one in five" chance Brexit will not occur.
The Liberal Democrat leader made the comments on Sky News, saying there was at least a "20% chance" Britain would not undertake a departure from the European Union.
He told Niall Paterson the "sheer complexity" of the issue, as well as internal divisions within the Government, could play a part in a shifting public attitude.
Cable suggested that by the middle of 2018, the issues posed by Brexit could result in the country and Parliament seeking a way to remain in the bloc, and suggested it was important to offer the public another vote once the Brexit landscape became clearer.
At the moment, negotiations with the European Union are deadlocked over issues relating to the Irish border, financial settlement, and citizens' rights.
Prime Minister Theresa May and the UK team are seeking to convince the EU to move onto discussions of trade by December, and have a week left to meet the EU's deadline.