There is no stipulation in the Postal Services Bill, which privatises the service, that the image should be included on future stamps. The monarch's head has been on every stamp since the Penny Black of 1840.
The Bill could result in up to 80 percent of the Royal Mail owned by a foreign company.
The leading bidders in the Royal Mail sell-off are expected to be Dutch and German operators.
The British stamps are the only ones in the world that do not carry the country's name - just the portrait of the sovereign.
The current standard stamps, drawn up in 1967 by Arnold Machin, are considered a design classic and a defining icon of Britain recognised around the world.