The family of the director, who died earlier this year, has been in talks with Warner Brothers, the film's distributor, which is eager to make it one of its prime releases next year.
Kubrick's adaptation of Anthony Burgess's futuristic novel of 1962 became a cause celebre on its release in Britain in January 1972. Though its violence was stylised, there was orchestrated outrage at the supposed glamorisation of the violent scenes; and there was no doubting that Malcolm McDowell, as the fashion- conscious, Beethoven-loving, intellectual gang leader Alex was a glamorous figure.
The Sun campaigned to have the film banned and more than one defence lawyer cited the movie as having a corrupting influence on clients charged with violent assault.
But the film ran for a year until January 1973 and made pounds 4m at the box office. Kubrick then decided to withdraw it because he and his family had received death threats.
A senior executive at Warner said yesterday: "Stanley did receive threats from strange people. And it was because of this that he withdrew the film, but only in Britain. He also stopped the video being released, though that too is available in other countries."
Talks with the Kubrick family were in their final stages and the film was likely to be released next year. "The family believe it would be a fitting memorial to Stanley."
Provided the film is released - and it will have to apply anew to the British Board of Film Classification - the video will be released six months later.
Over the past two decades, cinemas trying to show the film have been threatened with legal action by Warner Brothers. But now the company is desperately eager to show the film officially, anticipating that after Kubrick's death it will once more become cult viewing.
Alexander Walker, the film critic, biographer and friend of Kubrick, said recently that the director did not appear to have changed his attitude to the "ban" in the final years of his life. "He was not ashamed of it, but he still thought the time was not right."
Walker said there was a strong movement in favour of the re-release of A Clockwork Orange. "A couple of generations have grown up since it was last seen, and now the violence appears highly stylised."
In the film, a gang of thugs who rape, kill and use "ultra violence" are dressed incongruously in bowler hats.