The UK's biggest car union has asked MG Rover to appoint two independent directors to the board.
The T&G union said the group's directors had shown "morally unacceptable behaviour" in setting aside millions for their pension funds.
MG Rover said it would consider appointing a non-executive director if they found the right individual.
It added it had offered the head of the T&G union a non-executive director post in 2000, a claim the union rejects.
The carmaker is owned by the Phoenix Consortium, a group of four businessmen led by John Towers who bought it from BMW four years ago for £10, safeguarding thousands of jobs at its Longbridge plant.
But recently there has been concern about millions set aside in trust funds for the benefit of senior executives.
Concern has also been raised over reports on how the directors have structured the firm financially.
MG Rover's directors have strongly denied allegations of asset stripping.
But the T&G has said it would like to see all assets of the business brought back under the control of the MG Rover Group.
T&G general secretary Tony Woodley told BBC Radio Four's Today programme he thought the directors had done "an extremely good job in difficult circumstances" since they took over.
But he added that the putting aside of £10m for directors' pension trust funds was "morally unacceptable".
"The money that's been taken out of the company from our point of view is corporate greed and bad behaviour.
"What we've got to do now is... make sure that every bit of income, as limited as it is in this company, is used for building vehicles, and creating new models, maintaining jobs and keeping manufacturing in the West Midlands."
Mr Woodley said the appointment of independent directors would help to soothe any nerves about the company.
"There's a crisis of confidence out there and only the Rover directors can put that right now, in my view, " he said.
A spokeswoman for MG Rover told BBC News Online that the trust fund was "the main benefit of the four owners who had had no pension benefits since the company was set up in 2000".
She added that concerns about the running of the firm were unfounded as the new owners had managed to cut losses each year from a total of £378m in 2000 to £95m in 2002.
Asset-stripping allegations were also untrue, she said. The restructuring of the firm was necessary because of their different parts of the group had different business plans, teams and objectives.
The spokeswoman also said the firm would not be actively looking for a non-executive director.
But she added : "We will be willing to consider it if the right individual presents themselves.
"In 2000, Tony Woodley was offered the opportunity to take up such a post, but didn't."
However, the T&G denied Mr Woodley had been offered the position.
The latest call for a shake-up at the Birmingham-based firm comes four months after union officials from the T&G and Amicus held 'clear the air' talks with Phoenix Holding's chairman John Towers.
At the time, the T&G had said it wanted answers to questions about the financial restructuring of the loss-making car firm.
In November 2003, MG Rover's pension fund was reported to be £73m in deficit, news which coincided with the firm announcing a £12.9m trust fund had been set up for company executives.