NTL has raised its takeover offer for Virgin Mobile to £961m ($1.7bn) in an effort to break the impasse over the proposed deal.
NTL and Virgin Group are still in discussions
The two companies are in talks about the improved offer after Virgin Mobile rejected NTL's original £871m bid.
Sir Richard Branson, Virgin Mobile's main shareholder, has indicated that he would be prepared to receive both cash and NTL shares in a deal.
This could see him receiving less than minority shareholders.
However, the revised deal has yet to be approved by Sir Richard's Virgin Group, which owns 71% of Virgin Mobile, minority investors or Virgin Mobile's board.
But it is thought Sir Richard might be willing to accept the restructured offer in order to break the logjam in discussions.
Under a restructured offer, he could accept 67p a share in cash, in addition to NTL shares, while other shareholders could receive 372p a share in cash only.
If that happened, he could receive about £42m less than other investors.
Virgin Mobile rejected NTL's 323p offer in December and it is thought that some minority investors are holding out for a 400p offer.
In the balance
The deal is also conditional on due diligence and the two companies agreeing a deal over use of the Virgin brand on NTL products.
This agreement could be worth up to £10m a year to the Virgin Group.
If concluded, the deal would create a media company capable of challenging BSkyB, the UK's dominant pay-TV provider.
But one analyst said he believed the deal was far from done.
"I don't think it is a complete slam dunk given the noises that one of the larger shareholders has been making," Robert Grindle, telecoms analyst at Kleinwort Wasserstein, told the Press Association.