The survey, carried out by the Leave.EU campaign group, shows Mr Nuttall with a lead of 39 per cent in the Staffordshire constituency.
It predicts Labour's Europhile candidate Gareth Snell will finish second with 33 per cent of the vote.
Tory hopeful Jack Brereton, who also backed Remain, is projected to finish third, narrowly ahead of Lib Dem candidate Zulfiqar Ali.
Leave.EU – which is funded by Ukip donor Arron Banks – did not provide details of the poll methodology.
But it insisted it was a "major polling exercise" and said the sample size was greater than 4,000.
The by-election was triggered last month after the resignation of Labour's Tristam Hunt.
Ukip's Paul Nuttall is contesting the Stoke Central by-election
Mr Nutall, who replaced Nigel Farage as Ukip chief in November, hopes he can capitalise on Eurosceptic sentiment in the area.
His closest rival, Labour's Mr Snell, has angered locals by branding Brexit a "massive pile of s***" in a Twitter rant.
He hopes he can capitalise on Eurosceptic sentiment in the area
Nigel Farage in pictures
Thu, December 15, 2016
Nigel Farage is a British politician who has been the leader of the UK Independence Party since October 2016.
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British politician Nigel Farage arrives at Trump Tower on December 15, 2016 in New York City. President-elect Donald Trump and his transition team are in the process of filling cabinet and other high level positions for the new administration.
The by-election will take place on February 23.
Mr Nuttall has said a win in Stoke could "open the floodgates" for the party to win seats in the northern England and the Midlands.
He added: "I know that I can represent the views of voters in Stoke Central better than my opponents who supported Remain."
Nuttall says a win in Stoke could 'open the floodgates' for Ukip
Mr Farage is set to join his successor at a major rally as the by-election draws closer, according to Ukip sources.
Earlier this week Mr Nuttall defended Donald Trump amid a mass backlash against his controversial 'Muslim ban'.
He criticised calls from the "liberal, metropolitan" elite to ban the US President from making a state visit to the UK.
Nigel Farage is set to join his successor at a rally in Stoke
The MEP for North West England said: "I will say the idea we're not going to roll out the red carpet for President Trump is nonsense.
"We did for the King of Saudi Arabia and the President of China, a country which has human rights abuses as long as your arm.
"It's another case of liberal, metropolitan hyperbole."