Industry sources say NTL hopes to create a rival to the biggest cable company, Cable & Wireless Communications (CWC), which was formed from a pounds 4.5bn four-way merger in April.
The approach to Telewest, which is being spearheaded by NTL's head, Barclay Knapp, is at a very early stage. But both of the companies involved acknowledge that further consolidation is vital to revive the cable industry's fortunes.
This is the second time in two months that Telewest has been the subject of merger speculation.
At the end of June, the company was forced to play down comments by Telewest's chairman, Fred Vierra, that he could not rule out a merger with CWC.
Sources said United News & Media was keen to get involved with Mr Knapp's plans, although no one at United was available for comment yesterday. United already has a business relationship with NTL through its link-up with S4C - the Welsh Channel 4 - to provide services for the last remaining digital terrestrial licence.
The pair joined forces to bid for the licence, which carries the S4C and Channel 5 digital services but has half its capacity spare for new programming, after losing out to British Digital Broadcasting in the battle to win the three key digital terrestrial licences.
A spokesman for Telewest said last night: "We never comment on market rumours."
A spokeswoman for NTL reiterated that sentiment, but added: "We've made it very clear there will be further consolidation and in time there will be three or four big cable companies."
NTL has previously been the odd man out in the cable industry, going it alone where other companies have co-operated.
Telewest and CWC jointly ordered set-top boxes from General Instrument for the launch of digital cable television, but NTL was not involved.
The cable companies have been under pressure to provide a more united front to improve the uptake of cable television services.
At the last count, Telewest had built 66 per cent of its network, and had passed 2.6 million homes, but only 550,000 of those took cable television.
Around 720,000 homes used Telewest's telephone service, while roughly 430,000 subscribed to both television and telecoms services.