Pro-EU campaigners have said support is growing for a second referendum, while others, including Tory MP Heidi Allen and Labour MP Ali McGovern, have said Farage wants a second Leave to torpedo any notion of a soft Brexit.
He said that pro-Europeans such as former prime minister Tony Blair "will never ever ever give up".
"Maybe, just maybe I'm reaching the point of thinking that we should have a second referendum ... on European Union membership", he said, adding that leading Remain figures will otherwise "go on whinging and whining and moaning all the way through this process".
Explaining his comments to The Independent, Mr Farage said: "I'm considering the possibilities that this might have to happen, and I don't think Leavers should completely ignore the fact that it could".
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.
Meanwhile, in a reference to the 2010 leaders' debate, Nick Clegg tweeted: "I agree with Nigel".
The odds of Britain going back to the polls to decide whether it should remain in the European Union have significantly dropped in the past six months.
Lib Dem Brexit spokesman Tom Brake said: "Tony Blair and Nigel Farage aren't two people I'd normally like to be put in a group with, but on this issue they are speaking sense".
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Farage later backtracked from the notion that he actively wanted another referendum, but said leave supporters must "face this potential threat" and start organising for another campaign.
"The percentage that would vote to leave next time would be very much bigger than it was last time around".
Earlier yesterday in a TV interview Mr Farage revealed he was on the verge of a change of heart on a second referendum.
Steve Baker, a Brexit minister, said the former Ukip leader's comments were "further confirmation of my long-held view that Nigel Farage is one of the greatest impediments to a successful Brexit".
Farage's statement has some pro-EU activists fired up about potentially turning around 2016's vote to call it quits with the EU.
And Labour's Chuka Umunna said: 'For perhaps the first time in his life, Nigel Farage is making a valid point'.
"I am convinced that the Leave side would win a second referendum, should one be held, with an even larger majority".
"The people voted without knowledge of the true terms of Brexit".
"Many Remain voters can now see that the campaign led by the then Prime Minister and Chancellor was deliberately misleading".