The suggestions stem from the latest Hooper report in which the former Ofcom deputy chairman has argued that private sector capital and disciplines must be introduced in order to modernise the mail business
According to the report, the number of letters being sent has declined at a more severe rate than forecast in his original 2008 report, with a drop as high as 40% possible in the next five years.
Royal Mail's financial position has also worsened with an £8bn pension deficit "even more unsustainable than 18 months ago," he said in the report.
Hooper has recommended that a "less burdensome regulatory framework" needs to be introduced, movement of the pension deficit to the government and private capital through partnership, trade investment or an initial public offer.
Business secretary Vince Cable welcomed the suggestions and claimed that Hooper has painted "a very clear picture".
He said: "Royal Mail is facing a combination of potentially lethal challenges – falling mail volumes, low investment, not enough efficiency and a dire pension position.
"We are determined to safeguard Royal Mail for the future and help it tackle these challenges. We will come forward with new legislation in the autumn."
However, workers union CWU has claimed that any move to privatise Royal Mail would be "politically motivated".
Billy Hayes, CWU general secretary, said: "Privatisation would be devastating for Royal Mail and the whole country's postal services. The universal service has been a key part of the UK post for 170 years but because it isn't the profitable element of mail, the privatisation will put it at risk."
He added: "This could damage the service for all customers including millions of small business and potentially harm the UK economy.
"Privatisation will also mean separation of Royal Mail and the post office network, putting the very existence of many more post offices that play such a key role in Britain's communities at risk."
Concerning Hooper's calls for a new regulatory framework, Nick Wells, chief executive of TNT Post UK, said the proposal is essential to counter the monopolistic strength of Royal Mail".
He said: "Postcomm has done a reasonable job so far, but it has not been tough enough on Royal Mail on some issues that will enable true competition to take place in the UK.
It is important that the proposed new regulator, Ofcom, is firm and fair and has the detailed market knowledge and expertise necessary to supervise the currently monopolistic postal market."
Royal Mail set for privatisation or sale
Royal Mail will be privatised or sold off following recommendations from the former regulator Richard Hooper, the government has confirmed.