According to a Press Association report, the revised offer has been provisionally agreed by the board after weeks of negotiations, following the initial rejection of the cable firm's 323p-a-share offer, which valued the firm at £817m.
Independent directors in Virgin Mobile, who own 28% of the company compared with Branson's 72%, had been holding out for a higher offer.
Reports say that a three-way deal is set to be signed, with Branson agreeing to receive less than the minority institutional shareholders, which include fund manager Fidelity Investments.
Under the complex deal structure, it is understood that NTL is offering 360p a share for the whole group, with Branson offering minority holders another 12p a share, taking the price to 372p for the independent shareholders.
Once the deal has gone through, NTL, which recently completed its merger with UK cable rival Telewest in a £3.4bn deal, will rebrand under a licensing deal with Branson as Virgin Media.
NTL and Virgin Mobile declined to comment yesterday, as shares in Virgin Mobile closed up 3p at 371p.
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