The lure would be a substantial windfall - some say it could be as much as pounds 2bn - for a new government desperately seeking revenue but pledged not to increase income tax. That is why Gordon Brown, the Shadow Chancellor, is said to be tempted by the idea.
Last July Michael Grade, the channel's Chief Executive, wrote to Tony Blair to ask Labour's view. Mr Blair replied unambiguously: "Channel 4 is a success and I believe it would be wrong to place in jeopardy its achievements by privatising it."
Labour's policy document on media and the arts, published last month, pointed out that the channel has fostered 500 or more independent production companies, and declared: "It seems unimaginable that the Government could ever consider privatising the channel and thus jeopardising this resource."
Despite such seemingly clear commitments, the proposal persists partly because several of Labour's prominent supporters in the television industry are in favour of it. Lord Hollick, boss of United News and Media, Melvyn Bragg of London Weekend Television and Greg Dyke, of Pearson TV and Channel 5, are all identified with Labour and all have strong links with ITV.
Until 1990, the channel was effectively controlled by the ITV companies, which sold advertising on its behalf. Now it sells its own air-time but under a controversial "funding formula", is obliged to hand over part of its revenue to ITV. The Government has now agreed to phase the system out over the next few years.
This means that Channel 4 will be able to apply more of its revenue to developing programmes. Although obliged by its remit to cater for minorities it still wins about 11 per cent of the TV audience. Thus it eats into the advertising income of ITV companies already weakened by the arrival of Channel 5.
The ITV companies believe that if, like them, Channel 4 had to pay dividends to shareholders, they would be competing on a level playing field. Opponents of the idea say that, even if its remit notionally remained in place, privatisation would inevitably mean that the programmes would go down- market in the search for higher viewing figures.
Michael Grade and Sir Michael Bishop, chairman of the Channel 4 board, oppose privatisation. However, both men are stepping down this year.
Supporters of privatisation argue that Grade has drifted from the channel's remit by relying on American sitcoms to boost ratings. If the channel were privatised, they say, the Independent Television Commission could insist on a tougher remit being imposed.