He told the BBC he was hopeful the party could get "over the line in a number of seats".
But he would not be drawn on how many seats, or in which constituencies.
The party is standing in about half the number of seats contested in 2015. Its only MP in the last parliament, Douglas Carswell, defected in March.
Mr Nuttall said UKIP was campaigning strongly in seats where it has local councillors.
And he rejected suggestions the party was in decline, predicting that by the end of 2018, UKIP would be "bigger in terms of membership and higher in the polls than it's ever been before".
Asked about suggestions support for UKIP could cost the Conservatives seats, he told BBC Radio 2's Jeremy Vine he had struck deals with Brexit-supporting MPs from both the Tories and Labour, to help them retain their seats:
"In some places we have stood down in favour of a Labour MP," he said.
"People like Kate Hoey, for example, I don't want to see Kate Hoey not in the House of Commons because she's been a true Brexiteer all her life.
"What we need is for the prime minister to go into these negotiations strong, confident in our country and not prepared to backslide."
He also spoke about the Manchester attack and said that while the prime minister was not to blame for last week's bombing, Theresa May was responsible for cutting police numbers
Local police officers who are known in a neighbourhood were more likely to have the trust of the locals who would pass information to them, he said.
He also talked about banning Muslim women from wearing a full face veil.
He said he was "serious" about banning the veil in the UK and claimed that other countries in Europe were also going the same way.
He said such a ban was needed for greater integration, so that people could be identified on CCTV and also because of vitamin D deficiency.

A house and a number of cars in the city's Hazelbank area have been targeted in recent days.
It is believed youths fill a drain pipe with mud before launching it like a catapult at homes and vehicles.
Sinn Féin councillor Eric McGinley has called on those involved to stop immediately.
"Apart from the mess which has been created, there is a very real danger that an accident will occur if passing cars are struck by this debris," said Mr McGinley,
"When motorists are targeted it can cause damage to the car and could scare a driver into crashing, so there are very serious implications.
"Drivers have been in touch telling us that these incidents were taking place over the weekend."
Mr McGinley made a further appeal to parents in the area to be aware of where and what their children are up to.
"These muck bombs are going to detract from the general appearance of the area," said Mr McGinley.
"So, parents need to impress upon their children the dangers of their actions.
"I've been in contact with the housing executive about this and they have given me assurances that the mess will be cleaned up as quickly as possible," he added.
A spokesperson for the Housing Executive said: "There is a tenancy at this property and a number of issues have arisen, which we are currently working to resolve.
"We have taken measures to protect our property."
UKIP will win seats at the general election, even though they had no MPs at the end of the last parliament, its leader Paul Nuttall has predicted.
[NEXT_CONCEPT]
Drivers are being put in "very real danger" by youths throwing so-called muck bombs in Derry, says a local councillor.