The report comes just a week after the Republican presidential candidate reignited his feud with former Miss Universe winner Alicia Machado, whom he called "Miss Piggy" after she gained weight.

More than 20 people who worked with Trump on the high-rating NBC series – including contestants, editors and crew – made a series of allegations to the Associated Press.

Former producer Katherine Walker claimed the wealthy businessman questioned people about which contestants would be a "tiger in bed", and "frequently" talked about women's bodies.

Another crew member, who asked to remain anonymous, said Trump once singled out a woman in a boardroom and asked male contestants if they would "f--- her". He then announced that he would like to "f--- her", too.

"We were in the boardroom one time figuring out who to blame for the task, and he just stopped in the middle and pointed to someone and said, 'You'd f--k her, wouldn't you? I'd f--- her. C'mon, wouldn't you?'" The crew member continued: "Everyone is trying to make him stop talking, and the woman is shrinking in her seat."

Eight former crew members alleged Trump remarked on the "nice rear" of a camerawoman, and repeatedly made other lewd comments about her. He also compared her "beauty" to that of his daughter Ivanka.

In 2006, Trump told ABC's The View: "If Ivanka weren't my daughter, perhaps, I would be dating her."

The Apprentice – in which aspiring capitalists try to avoid being fired by Trump – is credited with turning the property developer into a global celebrity.

Walker recounted one conversation with Trump, in which they discussed firing a female contestant.

"He said, 'You mean the one with the' — and he puts his hands out in a gesture to signal the girl with the giant boobs. He didn't even know her name," Walker said, adding that the contestant, Kristi Frank, was fired at the end of the episode.

She said that after Trump delivered his punch line "You're fired!" he told her fiancé that "of all the girls," she was the contestant he would have chosen to marry.

In portions of the boardroom sessions filmed but never broadcast, Trump is said to have asked male contestants to rate the physical attractiveness of female cast and crew.

One former crew member – speaking anonymously, after signing a non-disclosure agreement – said: "If there was a break in the conversation, he would then look at one of the female cast members, saying 'you're looking kind of hot today, I love that dress on you,' then he would turn to one of the male cast members and say 'wouldn't you sleep with her?' and then everyone would laugh.

"There would be about 10 or 12 cameras rolling and getting that footage, which is why everybody was like, this guy just doesn't care."

While Trump had been gaining ground on Democratic opponent Hillary Clinton, he suffered a series of setbacks recently, including a weak performance in their first debate. Then The New York Times revealed he had declared a $A1.2 billion loss on his 1995 income tax return – a deduction so large, he could have avoided paying federal income taxes for up to 18 years.

Interviewed separately, The Apprentice's staffers agreed to recount their experiences of Trump's behaviour towards women because it had become a "core issue in the presidential campaign", the Associated Press reports.

Contestant Gene Folkes alleged that in one season, Trump called for contestants to wear shorter dresses that showed more cleavage. Several cast members also said Trump had one female contestant twirl before him so he could "ogle" her figure.

Randal Pinkett – who won the program in December 2005 and who has recently criticised Trump during his run for president – said he remembered the real estate mogul talking about which female contestants he wanted to sleep with, even though Trump had married former model Melania Knauss earlier that year: "He was like 'Isn't she hot, check her out,' kind of gawking, something to the effect of 'I'd like to hit that.' "

The Trump campaign has issued a general denial.

"These outlandish, unsubstantiated, and totally false claims fabricated by publicity hungry, opportunistic, disgruntled former employees, have no merit whatsoever," said Hope Hicks, Trump's campaign spokeswoman. "The Apprentice was one of the most successful prime-time television shows of all time and employed hundreds of people over many years, many of whom support Mr Trump's candidacy." She declined to answer specific questions that were emailed and declined an interview request.

Other cast and crew told the Associated Press they had "positive, professional" experiences with Trump and had never heard anything that had made them uncomfortable.

Jennie Finch, US softball star and former contestant, said Trump was "extremely supportive ... you could tell there was so much respect there on all sides, especially with female athletes".

Contestant Poppy Carlig, who performed the twirl, said it was just "playful banter".

"I don't immediately jump to the conclusion that people are having bad intentions with what they are saying. He said I reminded him of his daughter and I thought that was really touching because I know how much he values his family."

Twelve former contestants and crew members spoke on the record about what they described as Trump's inappropriate behaviour. Another nine said they did not want to be identified because they signed non-disclosure agreements, or were concerned about wrecking their careers or retaliation from Trump.

Trump points to his record of hiring women, but he has often been accused of sexist behaviour. At the first Republican debate, in August 2015, Fox anchor Megyn Kelly asked whether a man who has called women "fat pigs, dogs, slobs and disgusting animals" has the temperament to be president. After that debate, Trump attacked Kelly and her questioning, "You could see there was blood coming out of her eyes. Blood coming out of her wherever."

Rebecca Arndt, a camera assistant who worked on the show following Trump's 2005 marriage, said Trump would stop production to make comments about the camera operator's looks in front of the crew.

"I remember being in the foyer once with eight or 10 cameras set up and he said something about her being so pretty," Arndt said. "He would make it about his line of sight, like 'There is a beautiful woman behind that camera, so I only want to look at that.' It was supposed to be considered a compliment, but of course it was inappropriate."

Arndt said that Trump would publicly discuss the woman's beauty and how her blue eyes and blonde hair compared to his daughter Ivanka's looks.

"He would just mention it all the time. I remember him comparing Ivanka to her and saying that only Ivanka was prettier," she said.

One former contestant, Tyana Alvarado, said she wasn't offended when Trump told her she was attractive – but noted that he played by his own rules.

"Most men have to behave because they are in a workplace, but he could do what he wanted," Alvarado said. "In all jobs, people have to sign sexual harassment paperwork, but Mr Trump was putting on a TV show so he got to do it."

with the Associated Press