The Department of Culture, Media & Sport is understood to be considering the proposal by cable operator NTL, which still has 1m analogue cable subscribers.
The move would give analogue customers of NTL and those of rival cable operator Telewest access to BBC Three, BBC Four and News 24, which at the moment are only allowed to be carried on digital platforms.
The plan is likely to come under fire from the commercial sector because it contradicts one of the arguments that was used by the BBC when it was battling to win approval for the launch of its controversial youth channel BBC Three.
Speaking at the Westminster Media Conference last year, BBC chairman Gavyn Davies hit out at the government's decision to further delay the launch of BBC Three as detrimental to its plans to switch over to digital by 2010.
"Without BBC Three, our digital proposition looks much less compelling and analogue switch-off looks that much further off," he said.
The BBC's board of governors have approved the move because they are keen to get more people watching its channels. BBC Four and BBC Three have come under fire for not attracting enough viewers after the broadcaster spent £200m of licence-fee money on its digital services.
The move is also likely to be unpopular with BSkyB, which has spent £1bn building its digital satellite network in the UK and has already switched off its analogue service.
An NTL spokeswoman defended the move in the Sunday Telegraph. She said: "Obviously, we are encouraging people to take up digital TV services. However, these analogue customers are licence-fee payers... and we think they should have access to the BBC's digital channels."
As part of the deal, Telewest and NTL would have to agree not to offer analogue customers any of the extra services that come with BBC Three and BBC Four, such as interactive, text and audio services. However, interactive TV services are not available over analogue networks.
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