Internal analysis reportedly shows the number of outstanding faults with the ferries spiralled to 237 in March.
This is up from 166 before the nationalisation of Ferguson Marine shipyard in Port Glasgow, which is building the vessels, in 2019.
If issues are not resolved, there is a risk government ferries agency CMAL will not accept the ships.
A CMAL spokeswoman said it is “confident that outstanding issues can and will be rectified, and the vessels completed to enter service”.
There has been ongoing controversy over a botched contract to build two ferries at the Ferguson shipyard.
The vessels, the Glen Sannox and the as-yet-unnamed hull 802, are at least £150 million over budget and five years late.
The Herald on Sunday reported that an internal analysis by CMAL in March said some 65 per cent of the 237 outstanding faults relate to safety, maintainability or specification requirements.
The agency said resolution of the faults "is considered crucial prior to vessel handover”.
Scottish Conservative transport spokesman Liam Kerr said: "The SNP's mishandling of the ferries is a national scandal and the stink of corruption is growing.
"Years late and massively over budget, it now appears CMAL could reject Glen Sannox and Hull 802.
"Under scrutiny at Holyrood last week, Nicola Sturgeon's attempts to push all the blame on to a former minister reeked of desperation.
"Meanwhile, islanders can't get to work, hospital or get on with life as normal.
"The people of Scotland deserve answers and they deserve a public inquiry into this sordid mess."
A CMAL spokeswoman said: "The appointment of a permanent chief executive at the shipyard has been a welcome development, and we have further strengthened collaboration between our senior teams via the secondment of our senior vessels project director, which will provide added experience and expertise and improve decision making.
"We will continue to work in partnership and remain committed to the completion of the two ferries.”
A spokeswoman for Ferguson Marine said: “We are aware of legacy issues and as such have factored them into the amended plan being driven by the new CEO with the support of management and working closely with workforce representatives and CMAL to ensure high standards of workmanship, health & safety compliance, and morale.”
A Scottish Government spokesman said: “The Economy Secretary [Kate Forbes] has been crystal clear on what she expects from Ferguson Marine in terms of delivering the ferries, as well as turning the business around to be competitive.
“Until those vessels are serving the communities for which they were built, we will not let up in our drive and determination to get them finished and delivered. The board recognises that and has been driving that improvement process within the business.
“A senior member of CMAL staff has recently been seconded to Ferguson Marine management to support delivery of the vessels and resolve any outstanding issues.
"Working alongside the new chief executive, this has driven significant improvements already.
“We remain fully committed to completing these vessels, and it is important that the workforce at Fergusons also know that we remain committed to this work.”