There is reportedly a growing feeling among many political and media figures that the Trust is now incapable of bringing the BBC Executive to account on a range of issues.
According to The Times, documents revealed under the Freedom of Information Act demonstrate how BBC management is often able to "fact check" Trust investigations before they are published.
Sources within the BBC also reportedly viewed the Trust's launch of an impartiality review of BBC science coverage just two weeks before its year of science kicked off as a mark of pettiness from the governing body.
Should the Tories secure power at the election in May then the Trust would be stripped of its BBC branding and renamed the "licence fee payers trust", with a primary function under Section 23 of the Royal Charter to represent the interests of licence fee payers.
Under the new system, a non-executive chairman would be appointed to work alongside BBC director general Mark Thompson to stand up for his interests during times of crisis.
The approach would not involve a long-rumoured scrapping of the Royal Charter before it expires in 2016, but would see Lyons leave his post before the end of his four-year term in April 2011.
Even though the Tories are not publicly calling for the chairman to quit, the party is understood to privately believe that he will leave his post before being pushed.
The Tories hope that the new arrangements would usher in a transformation of BBC leadership culture without the need for wholesale changes to legislation. A former BBC director-general told the newspaper: "They can do that without having to change the law. You could do this on day two in office."
The latest report is part of an alleged groundswell of opposition to the BBC's governing body fuelled by a spate of recent controversies, such as the 'Manuelgate' scandal on Russell Brand's BBC Radio 2 show.
Last month, a report by centre-right thinktank Policy Exchange called for the Trust to be abolished in favour of a Public Service Content Trust covering all public service broadcaster output.
Former BBC director general Greg Dyke, who is running a review of the creative industries for the Tories, recently pushed for similar policy approach, with the added option of Ofcom taking on regulation of the BBC.
In a speech last year, Dyke described the Trust as "unduly slow and bureaucratic", as well as being expensive to run and the source of "inbuilt conflict" at the corporation.
However, its not just the political right in opposition to the Trust as culture secretary Ben Bradshaw recently described the organisation as being not a "sustainable model in the long-term".
He added: "I know of no other area of public life where the same body is both regulator and cheerleader."
In response to the latest media reports, a BBC Trust spokesman said that the organisation will not be drawn to "comment on speculation".
"What matters to audiences is that they receive quality content and services from the BBC," he said. "To that end the trust and Sir Michael are getting on with the job of getting the best out of the BBC for licence fee payers."