He will also ask Treasurer Josh Frydenberg to ask the Australian Securities and Investment Commission to stop the company from destroying its books, as it winds up.

Australian Communications Exchange is now under external administration after losing the contract for the National Relay Service - which provides captioned telephone services for deaf or hard-of-hearing Australians - last year.

But the woes for the company do not end there.

Mr Fletcher wrote to Assistant Minister for Charities Minister Zed Seselja on Monday, urging him to ask Australian Charities and Not-for-profits Commissioner Gary Johns to investigate to investigate Australian Communications Exchange.

It follows reports Australian Communications Exchange paid companies owned by a former director consultancy fees of nearly $360,000.

Brisbane financial adviser Scott Summers was still a director of AccessComm - a legally separate but linked company - at the time of the payments, the Australian Financial Review reports.

Former Australian Communications Exchange chief executive Sandy Gilliland and secretary Karolyn Niukkanen referred all questions to their liquidator, Bill Karageois who refused to address concerns about the company's use of funds.

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It follows years of questions about consultants fees and money being moved between related entities.

Mr Fletcher said he was concerned Australian Communications Exchange and its associated entities had used funds for non-charitable purposes, such as for the private benefit of its members, directors or staff.

Mr Fletcher also asked the charities watchdog to investigate whether the company's officeholder's failed to disclose any perceived or actual conflicts of interest, and failed to act in the best interests of the charity.

"I understand that the ACNC has previously investigated ACE and had a number of concerns with ACE's compliance with the Australian Charities and Not-for-profits Commission Act 2012 and the Australian Charities Not-for-profits Commission Regulation 2013," Mr Fletcher wrote.

The charities regulator is independent of government and cannot be directed to undertake an investigation by a minister.

The Australian Securities and Investment Commission will also be asked to consider preventing liquidators from destroying Australian Communication Exchange's books.

The company instructed liquidators to seek consent from ASIC to do so as it winds up in the wake of the contract loss.

The Morrison government went to market for a new provider for the National Relay Service last year, citing years of cost overruns.

The tender put out for the National Relay Service in 2017 was capped at $22 million per year, despite the service costing $31.2 million to deliver in 2017-18 and $32.2 million the year before.

Mr Fletcher told Parliament last year Australian Communication Exchange tried to almost double the cost per minute rate charged to taxpayers, from their then current rate of $4.44 to $7.49 during the tender process.

Mr Fletcher said the company tried to "leverage" the fact it had an exclusive licence to the CapTel technology in Australia to justify the increase.

Mr Fletcher also accused a company associated with ACE of actively marketing handsets to residents of requirement homes, leading to a a "sharp increase" in the number of call minutes from CapTel devices, which drove a cost blowout for the relay service.

However AccessComm spokesman Tony Bennetts said at the time the rise in CapTel minutes was not being driven by AccessComm trying to boost its customer base, but by Australia's ageing population.

The switch to Concentrix was fiercely opposed by users of the service, who preferred the CapTel handset to teletypewriters.

However the US owner of the technology, Ultratec refused to allow Concentrix to use the technology.

Ultratec has since offered to keep supporting CapTel handsets indefinitely using a US call centre, although the Australian government has warned this could cut out at any time and raised questions about the data and privacy controls in place.