Nigel Farage's successor is bidding to be elected in Stoke-on-Trent Central at a by-election contest on February 23.
The Staffordshire seat has been held by Labour since 1950 but, with nearly 70 per cent of local voters backing Brexit on June 23, Mr Nuttall revealed his message of a "clean Brexit" was receiving a "great response".
On Wednesday night, MPs are due to hold a final vote on the Government's proposed Article 50 Bill, which would hand the Prime Minister the power to formally notify the EU of Britain's departure.
Labour leader Jeremy Corbyn has ordered his MPs to vote in favour of the legislation at the Bill's third reading but could be facing another sizeable rebellion.
A total of 47 Labour MPs defied Mr Corbyn's three-line whip and attempted to block Brexit at a previous vote on the Article 50 legislation in the House of Commons last week, while shadow home secretary Diane Abbott – a close ally of the Labour leader – sparked a row by abstaining from the vote citing illness.
Shadow business secretary Clive Lewis has already threatened to quit Labour's top team in order to vote against the Bill tomorrow if none of the party's amendments are accepted.
Labour will attempt to add clauses to the short Bill this week, including a demand for the Government to regularly report back to Parliament during EU divorce talks, providing guarantees for EU nationals in the UK and protections for workers' rights.
Mr Corbyn has claimed he will be "lenient" on last week's rebels, despite convention suggesting the 13 shadow ministers who defied him should be sacked.
Ukip leader Paul Nuttall said he didn't think "anyone" knew Labour's position on Brexit
It's a bit like the hokey-cokey isn't it? You're in, you're out, you shake it all about.
Speaking to Express.co.uk from his campaign headquarters in Stoke-on-Trent, Mr Nuttall claimed any possible attempt by senior Labour figures to dodge a decision on Article 50 by abstaining on Wednesday would be a "pretty big gift" for Ukip.
He said: "It would be be a pretty big gift, in fact we probably couldn't ask for anything more.
"It will be very interesting, not just what Jeremy Corbyn does, not just what Diane Abbott does, but a lot of these Labour MPs that are sitting in Leave constituencies."
Mr Nuttall added any attempt by Labour MPs in Brexit-supporting constituencies by attempting to block Brexit and "subvert the will of their constituents" would see them placed on a Ukip hitlist at the next general election.
He said: "We will come after these people. We will ensure, we will try to ensure they lose their seats in 2020."
Jeremy Corbyn is facing another revolt by Labour MPs
The Ukip leader claimed he didn't think "anyone" knew Labour's position on Brexit.
Gareth Snell, Mr Nuttall's Labour rival in Stoke-on-Trent Central, has previously described Brexit as a "pile of s***".
Mr Nuttall said: "It's a bit like the hokey-cokey isn't it? You're in, you're out, you shake it all about.
"Corbyn seems to have lost complete control over his parliamentary party. Rebels were first going to be kicked out, now they're going to be let back in, there was 47 last week, there could be in advance of 80 this week.
"The party is a complete shambles when it comes to the EU issue, which is good for us in this seat because it's clear if you want clean Brexit, proper Brexit, what you voted for on June 23, you have got to go with Ukip."
Mr Nuttall claimed Ukip are "getting a great response on the doorstep" in Stoke-on-Trent Central.
He said: "Of course the majority of people here voted to leave the EU and they're quite clear what kind of Brexit they want.
"They want a Brexit whereby we control our own borders and our own monies. And that's not some sort of half-way house Brexit, some mealy-mouthed Brexit, it's a clean Brexit."
Theresa May's Brexit plan
Mon, January 16, 2017
It's finally here!
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Continued cooperation with the EU to tackle terrorism and international crime.
Mr Nuttall also highlighted concerns about local NHS services as a big worry for voters.
He said: "The local hospital is a huge issue.
"There are serious concerns about people waiting too long for beds and what we're saying is the NHS needs a quick cash injection and we'd do that by taking money from the bloated foreign aid budget."
The Stoke-on-Trent by-election was sparked by previous MP Tristram Hunt, a critic of Mr Corbyn, quitting Parliament in order to take a job with the V&A Museum.