The Home Office is lining up A4e for another major government contract, despite the jobs agency being at the centre of a fraud inquiry, according to the investigative website Exaro.

Ministers have made the firm – owned by David Cameron's fallen "family champion" Emma Harrison – the preferred bidder to take over the Equality and Human Rights Commission (EHRC) helpline to advise people of their rights in discrimination cases.

Ministers ordered an audit of all Whitehall contracts with A4e to run alongside two police inquiries over allegations of attempted fraud involving the company. The Department for Work and Pensions, which provides most of A4e's UK income, is also investigating.

A4e has been "preferred" for the contract over Sitel, which ran the disability helpline for the EHRC before it was taken inhouse, and also over Citizens Advice and Vertex.

The privatisation of the helpline was sought by the Home Office and the Government Equalities Office. It costs £2.1m a year to run, employs 85 staff in Birmingham, Cardiff and Glasgow, and handles 50,000 calls and 15,000 emails every year. Staff are trained to provide detailed advice on discrimination issues covering disability, gender, race and sexuality, and advise on mediation services.

One service, which supported disabled passengers acting against operators they said had breached an EU directive protecting their rights when travelling by air, ended abruptly last month.

"Unfortunately due to our funding being cut we are no longer able to offer conciliation for cases related to EC Air Regulations 1107. Therefore we are unable to intervene in your case," the EHRC has told people contacting them.

Despite government guarantees that existing staff can apply to keep their jobs, many will be laid off because they are disabled and will not be able to relocate easily from Cardiff and Glasgow.

Mark Serwotka, general secretary of the Public and Commercial Services Union, which opposes the privatisation, said: "Speculation about A4e's involvement in plans to privatise the EHRC helpline have fuelled concerns about what is a totally unnecessary and damaging selloff.

"Instead of selling this vital lifeline for some of the most vulnerable people in our communities, the government should be investing to ensure people get the help they need, particularly at a time when its wider spending cuts are threatening to make our society even more unequal." The EHRC said the decision to outsource the service was taken by the Government Equalities Office after its review in late 2010.

"The commission was consulted on the tender specification and was asked to score one question on the tender responses."

The Home Office has defended the privatisation, saying: "The new advisory and support service will offer more in-depth support than the EHRC's helpline. Funding for free legal advice on discrimination will continue to be available through legal aid.

"The decision to stop funding the EHRC's helpline and grants system was taken because they did not represent value for money or support the commission in carrying out its core functions."

On Tuesday A4e said in a statement to Exaro: "The Home Office procurement process for this contract has not concluded as yet. We have not been informed that we are a preferred bidder. Given that the process is ongoing, you would not expect us to comment on the detail of our bid."

Harrison quit as chair of the company, which she set up, and has stepped down as the coalition government's "family champion", a voluntary role aimed at helping long-term unemployed families, after the firm called in independent auditors to check its accounts.

Thames Valley police have arrested five former employees on suspicion of fraud as part of its investigation. There are two other police investigations into allegations of fraud linked to the company, although the latter is believed to involve a subcontractor.

An internal audit report, leaked to BBC2's Newsnight programme, concluded: "Potential fraudulent or irregular activity is not confined to one particular geographical area … and shows a potential systematic failure to mitigate the risk towards this behaviour at both an office and regional level."

A4e said in a press statement earlier this month: "The board has made consistently clear in all previous statements that we take any allegations of fraudulent or otherwise illegal activity extremely seriously. There is absolutely no place for this type of misconduct at A4e.

"We obviously acknowledge the concerns raised by DWP, and we welcome and will co-operate fully with their planned investigations."