Donald Trump may have criticised illegal immigrants in campaign speeches, but three immigrant models who say they worked illegally for one of his companies claim they were treated like "slaves" by the agency which helped them skirt immigration laws.

The foreign models revealed to Mother Jones that they were employed by Trump Model Management without proper work visas. Two said they were instructed by Trump's modelling agency to lie to Customs' officials at the border about why they were visiting the US.

Once in the US and working illegally on short-visit tourist visas, Canadian-born model Rachel Blais and others talked of long hours and sky-high rents in cramped, overcrowded model dormitories that they were assigned by the agency.

"It's like modern-day slavery," Blais told Mother Jones, adding that the Trump operation was the "most crooked agency I've ever worked for, and I've worked for quite a few."

Two other models requested anonymity to avoid prosecution. Documents included in a recent lawsuit filed by a fourth former Trump model reveal that she also worked for Trump's agency in the US without a proper visa, the magazine reports.

When Blais arrived in 2004 from Montreal without a working visa she was sent to jobs and put up to one of Trump's models' apartments in Manhattan at high rents, she said. At one point she paid $1,600 a month for a bunk in a room that she shared with five other models, according to her financial records.

"We're herded into these small spaces," another of the models said. "The apartment was like a sweatshop."

"Most of the girls in the apartment that were not American didn't have a work visa," recalled Blais, 31, who worked for the Trump agency for three years.

The company eventually secured an H-1B visa for Blais allowing to work legally, but only went to bat for models who had forged a successful track record.

In the sixth-month gap before Blais was able to obtain a legal working visa, she brazenly appeared on national TV on Trump's reality TV show, The Apprentice, walking on a runway in clothing designed by his business protégés, notes Mother Jones. Trump looked on from the front row in a scene from the programme.

Trump has earned nearly $2m from the modelling company, in which he holds an 85% stake, according to the candidate's May financial disclosure filed by his campaign. The candidate's campaign spokeswoman Hope Hicks refused to answer questions about illegal foreign workers at the modelling agency.

"That has nothing to do with me or the campaign," she told Mother Jones.

Trump is planning a major speech in Arizona on where he stands on the immigration issue following recent shifts in policy. It's not clear if he will address the model issue.