The idea is currently being considered by Royal Mail pension chairman Jane Newell. However, although Newell has the power to close the scheme the final decision to do so is with Royal Mail management.
The existing pension scheme has a deficit of £3.4bn, while a revaluation of the fund's assets is expected to reveal this is closer to £10bn.
This would triple the amount of money Royal Mail would need to contribute to the fund.
It is highly likely the Communication Workers Union, representing postal workers, and Unite representing mail messengers, would call a nationwide strike if such plans to scrap the existing scheme come to fruition.
London postal workers begin a three-day strike this week.
The government has been under pressure to explain how Royal Mail is expected to manage its pensions deficit now that plans to part-privatise the postal group have been shelved.
The government had planned to pay off the group's deficit, which is expected to rise from the £3.6bn reported in 2006 to £9bn or more later this year, as part of the part-privatisation deal.