According to several reports, Telewest is planning a trip to New York to decide on the line-up of financial advisers and NTL is already understood to have asked Goldman Sachs to advise on the merger.
Of the two cable firms, NTL is by far the biggest with 3.1m subscribers compared with Telewest's 1.8m subscribers.
If the companies do merge it will form a powerful competitor to BSkyB, which announced last week it had added 100,000 subscribers to reach 7.7m homes in the UK.
A merger is likely to go through with few regulatory difficulties because there is little or no geographical overlap in the two services.
Cob Steinham, Telewest's chairman, is understood to be keen to see the merger go through quickly because he has the backing of US fund manager Bill Huff, who is Telewest's largest shareholder and the second biggest owner of NTL.
An announcement is expected on Thursday, when Telewest unveils its full-year financial results.
The merger was last mentioned in 2003 when Telewest managing director Charles Burdick said a merger with NTL could happen in the beginning of 2004.
However, although both companies have talked about a merger being a logical move, little concrete steps have ever been taken.
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