Virgin Mobile's board has rejected an £817m ($1.4bn) bid from cable operator NTL, despite the deal being backed by major shareholder Sir Richard Branson.
The company, 72%-owned by Sir Richard, opposed the offer on the grounds that it undervalued the business.
Analysts said the decision suggested Virgin Mobile was now hoping that NTL would return with a higher offer.
Sir Richard, meanwhile, said it was up to NTL's board to ensure a fair bid but he was 90% sure a deal could be struck.
NTL hopes to add Virgin's mobile phone facilities to its existing offering of TV, fixed line phones and broadband.
Richard Branson owns 72% of Virgin Mobile though his Virgin Group, whose representative on the Virgin Mobile board, Gordon McCallum, absented himself from the decision to reject NTL's approach.
"The board has concluded that the potential offer materially undervalues Virgin Mobile," the company said in a statement.
"It's for the board to negotiate with NTL a fair price for the shareholders, particularly the smaller shareholders. They have said to me they have quite bullish forecasts which they want to put in front of NTL," Sir Richard told BBC's Radio 4 Today programme.
"It up to them to negotiate a price that they feel is fair and we're happy to let them do that."
Sir Richard added that the actual difference was only about £25m, and he was confident a deal would still be struck.
"Since the combined group will be worth about £5bn my gut feeling... is that some sort of compromise will be reached. Everyone sees the logic of the deal, that it will provide great benefits for consumers," he said.
"I don't think NTL are going to fall out over what is a relatively small sum of money."
When asked what he thought the chances of a deal being struck were, he told the BBC: "If I was a betting man I would say it would be over 90% (chance), though obviously I may be wrong."
Some analysts reckon Virgin Mobile is looking for a white knight bidder to come forward.
"Virgin is trying to start a bidding war by rejecting the offer on the premise that the price isn't right rather than saying the company is not for sale," said Charter Equity Research analyst Ed Snyder.
NTL said on Monday that it had approached Virgin Mobile about a bid, and that it had the support of Virgin Mobile's network provider T-Mobile.
The cable operator has TV, telephone and internet customers in about five million UK households, and in October announced plans to merge with rival firm Telewest.
Virgin Mobile is the UK's fifth-largest mobile phone carrier and has more than five million customers.