Arron Banks, who funded the Leave-EU campaign, made the allegations in a new book called 'The Bad Boys of Brexit'.
The party called the claims "entirely false".
He claimed the DUP asked for £30,000 a month over four months to back his Leave.EU campaign.
He alleged he told the DUP they must be "joking" and said he made it clear "that's not the way we operate."
Mr Banks also claimed the DUP eventually got paid £50,000 a month for backing another campaign, Vote Leave.
The DUP has strongly denied the claims by Mr Banks, who recently accompanied his friend Nigel Farage on his meeting with President-elect Donald Trump in New York
They claimed Mr Banks had, indeed, offered them financial support if they changed which bidder they backed.
"The party neither accepted money from Arron Banks nor changed its mind," it said.
Vote Leave has also denied the allegations.
The DUP claimed that if any other campaign had been the designated lead campaigner for leave, the referendum would have been lost.
Mr Banks declined to give the BBC an interview.
The DUP has denied a claim from a multi-millionaire who poured millions of pounds into the campaign for the UK to leave the EU that they demanded money to back him.