In a wide-ranging interview with New York Magazine, the longtime British broadcaster and journalist says he first met the future US president at Rupert Murdoch's Christmas party in Aspen, Colorado in 1986, when Mr Trump told Neil —then the editor of The Sunday Times — to put him on the cover of the magazine.
He last saw the future president at Mar-a-Lago in 2015: "And I said, with full confidence, 'You're not going to run, are you? 'Cause you've got no chance of winning'", he remembers saying. "He said 'I know, but think what it'll do to my speaking fees. I'll get more than Bill Clinton!'"
Neil also claimed that Mr Murdoch, whose own media empire includes the president's mouthpiece Fox News, had "never rated" Mr Trump as a businessman "and doesn't rate him as a politician".
The Australian mogul is "used to having someone in Australia or in Britain that he's pretty close to and he's never really had that in America, and now he has" with Mr Trump, according to Mr Neil.
Neil, chairman of Press Holdings Media Group, which owns The Spectator, said that like UK prime minister Boris Johnson - once editor of the magazine - the "rules that apply to nearly every politician don't seem to apply" to Mr Trump.
There's precedent for Mr Trump to rake in a fortune after he leaves office in public speaking fees alone. It has become a lucrative industry for former White House officials, who have turned their time in public office into multi-million dollar enterprises.
The Clintons, former president Bill and 2016 candidate Hillary, earn more than $200,000 per speech.
George W Bush earned millions of dollars within the first few years after he left the White House.
Joe Biden earned more than $2m from his speaking appearances within the two years after his vice presidency, while Barack Obama famously earned $400,000 for a September 2017 speech to Wall Street firm Cantor Fitzgerald.