A union representing cleaning staff, United Voice, has accused Dimeo Cleaning Services of possible "unconscionable conduct" if the documents included a contract, asking the industrial umpire to deal with the matter.

Cleaners say they are awaiting written offers of employment from the company, and the department overseeing Parliament House said it told Dimeo it must give staff enough time to seek advice and support before signing employment documents.

Cleaning staff feared losing their jobs, having their shifts changed, or going onto probation after Dimeo emerged earlier this month as the winner of the $46 million contract to clean Parliament House inside and outside.

Staff working for the outgoing indoor cleaning contractor, Limro, say they have received verbal job offers from the new company but were asked to sign documents and provide bank account details and passport numbers before they received a written job offer or contract.

Cleaners said they were later told they could bring a family member, or someone they trust who could read English better, to Parliament House so they could interpret the documents before signing.

Many speak English as a second language, and United Voice said Dimeo would not provide it the documents.

The Department of Parliamentary Services said some cleaners had signed documents in an "applicant induction pack", but these were not an offer of employment.

Thelma Garcia, who has cleaned the building's rooms for 24 years and whose first language is Filipino, said she had never encountered a similar situation.

She was verbally offered a job and six months' probation, despite her length of service.

"I'm so upset really, I'm so upset," she said.

Chanmala Souksavat, whose first language is Lao, will bring a family member to read the documents Dimeo has provided.

"If they give us the form for home, it's better," she said.

United Voice has asked the Fair Work Commission to deal with the matter, saying Dimeo met the cleaners on May 21 and asked them to sign forms but did not let them take copies away for interpretation.

It said members did not know what they signed and that if the document was a contract, it would be "unconscionable dealing and/or unconscionable conduct" against the law.

"This is because by presenting documents to workers which they could not read or understand Dimeo took advantage of the existence of a special disability," United Voice told Fair Work.

It is understood the documents included information about a code of conduct and asked cleaners if they had any physical conditions.

Dimeo did not respond to questions from Fairfax Media on Thursday but has previously referred them to the Department of Parliamentary Services.

The department said Dimeo had advised it would make any offers of employment, setting out terms and conditions, separately to the "applicant induction pack".

"Dimeo has confirmed that those receiving offers will be welcome to take contract documents away for consideration or independent advice prior to accepting an offer," a spokeswoman said.

Dimeo had told the department it had begun meeting individually with Parliament House cleaners to allay any immediate concerns.

"Potential employees have been given an opportunity to have support people, family members or the union present at their face-to-face meetings with Dimeo," the department said.

Workers paid above the award will be re-employed at their existing rate, it said.

Dimeo had "expressed an intent" to offer all cleaners jobs that met their employment conditions, and the department said it understood the company had tried to contact all staff.

Cleaners, United Voice and Dimeo will meet at Parliament House on Friday and Fair Work will hear the matter on Tuesday.