The Labour leader was warned this weekend his party could lose millions of voters if he did not commit to the option of giving the public a second vote.
Farage, a current Member of the European Parliament and former leader of the UK Independence Party (UKIP), was one of the leading lights of the campaign for the UK to leave the European Union before the divisive referendum.
"If, on the other hand, we do offer clarity and a confirmatory ballot, we could do very well".
Labour's current stand is to keep all options on the table - including pressing for a further European Union referendum.
Duncan Smith has now requested that she stands down in May and described talks with Labour as a "recipe for disaster".
"In my view that clear and simple message should be that there should be a confirmatory vote of the British people".
The British cabinet office minister who is leading the Brexit talks between the government and the Labour party has said discussions on a compromise deal will continue this week, but they can not be allowed to drag out for too long. He then said they would "take stock" on the process once parliament resumes after its Easter break.
David Lidington, who is leading the talks with Labour on subjects such as environmental standards, workers rights and the security relationship with the European Union, said the discussions were going to continue next week but that they wouldn't last months.
He added that discussions couldn't be allowed to "drag on" for an extended period but continued to defend the prime minister's position.
"A second referendum still went down to defeat and I just question whether there is a majority for it in the House of Commons".
He said meetings later this week would be divided into different subjects led by relevant ministers and their Labour opposite numbers.
Although the Labour leader has avoided addressing the question so far, it could look like Mr Corbyn will avoid backing the Brexit option of giving the public a second vote.
"What the prime minister has to do now is aim everything towards departure before the euros (European elections) which would then allow her to step away having done what she said she would do - get the United Kingdom out of the European Union one way or the other", he told Sky News.