Appearing on The Wright Stuff on Channel 5, he said: "My mind is actually changing on all this".
The former Ukip leader said Remainers such as Nick Clegg, Tony Blair and Lord Adonis 'will never, ever, ever give up.
Ukip's Brexit spokesman has told LBC Nigel Farage's suggestion of a second referendum is "attention seeking".
Nigel Farage's surprise call for Britain to prepare for a second European Union referendum has ignited hopes among anti-Brexit campaigners that both sides of the debate will back a poll on Theresa May's final deal. The percentage that would vote to leave next time would be very much bigger than it was last time around.
Nigel Farage has called for a second Brexit referendum to end the constant stream of negativity about the decision to leave the European Union from an increasingly vocal group of pro-European campaigners form across the political spectrum.
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Britons shocked the political establishment in June 2016 by voting 52 to 48 percent in favour of ending more than four decades of political, economic and legal ties with the EU.
He has a large groundswell of support in the United Kingdom, both among the public and other pro-Brexit politicians, so what he says is likely to carry weight.
In an interview with The National, Mr Blair said the vote could take the form of either a referendum or a national election.
"Our mission is to persuade them to do so", Blair said at a pro-EU Open Britain event last February.
Mark Malloch Brown, a peer who chairs the Best for Britain campaign, said another referendum was "something that the country needs".
Liberal Democrats made a second "exit from Brexit" vote a plank of their 2017 campaign.
Hours after arguing that another vote would silence those "whinging and whining" who are against leaving the bloc, and with the idea drawing immediate support from pro-EU politicians, he sought to clarify his comments and reversed course. Previously he has insisted that the result of the 2016 referendum had to be respected.