In an interview with the Mirror the Ukip leader said such a narrow margin would prompt him to fight for a second referendum.
He said: "In a 52-48 referendum this would be unfinished business by a long way. If the remain campaign win two-thirds to one-third that ends it."
Britain voted to leave the EU with a 52-48 split.
Nigel Farage has not suggested a second referendum.
Many other people are however.
We the undersigned call upon HM Government to implement a rule that if the remain or leave vote is less than 60% based a turnout less than 75% there should be another referendum.
Demand meant the petition website was temporarily unavailable on Friday morning.
Leave won 51.9% of the total vote to Remain’s 48.1% after the final count. Turnout in the referendum was 71.8% - with more than 30 million people voting.
Despite an on-the-day poll predicting a win for Remain, Leave voters turned out in droves in order to take the UK out of the EU.
The decision has already sent shockwaves around the world and prompted the resignation of David Cameron.
Another petition using the hashtag #londependence calls on Sadiq Khan to declare London independent and rejoin the EU.
London is an international city, and we want to remain at the heart of Europe.
Let’s face it - the rest of the country disagrees. So rather than passive aggressively vote against each other at every election, let’s make the divorce official and move in with our friends on the continent.
This petition is calling on Mayor Sadiq Khan to declare London independent, and apply to join the EU - including membership of the Schengen Zone (Umm, we’ll talk about the Euro...).
Mayor Sadiq, wouldn’t you prefer to be President Sadiq? Make it happen!
So far it has gained 110,000 signatures.
Reid quizzed Farage on whether he could guarantee the bold pledge promoted on the side of a much-photographed battle bus would be delivered on.