Verizon is contemplating a roughly 50:50 cash and stock bid for the 45 percent stake in Verizon Wireless it does not already own, an asset it has long coveted, the sources said. It has not put a proposal to Vodafone yet but has hired banking and legal advisers for a possible offer, the sources said late Wednesday.

There are no guarantees that Vodafone will be interested in a deal or that any bid will materialize, the sources said. But they said Verizon was ready to push aggressively and hoped to start discussions with Vodafone soon for a friendly agreement. Verizon is also prepared to take a bid public if the British company does not engage in talks, one of the sources said.

A Verizon spokesman declined to comment. Vodafone declined to comment. Verizon Wireless was not available for comment.

Shares in Vodafone, the world's second-largest mobile operator, rose 1.6 percent in London, while Verizon shares were up 2.5 percent in New York.

Verizon, which has made little secret of its wish to buy out its British partner in the biggest U.S. mobile operator, has ramped up the pressure in recent months, saying that it believed it could buy the asset in a tax-efficient way. The company's move to hire advisers and the sources' revelation of a price range highlight the company's seriousness about doing a deal.

At $100 billion, a deal would be the third-largest acquisition ever, according to Thomson Reuters data, and would come amid a new round of industry consolidation.

DEAL FUNDING

Investors say the conditions for a deal have improved as a result of Verizon's strong results, its share price gains, and low interest rates. Verizon shares are valued at 17.9 times forward earnings, compared with a multiple of m11.8 for Vodafone.

"It would depend on how the deal is structured and what the cost of financing is. But we think the deal at $100 billion would be viable for Verizon to do," said Louis Cimino, portfolio manager at Reaves Asset Management in New Jersey, which owns about 1.8 million Verizon shares. He said he would support a deal even if the price rose to $120 billion.

The sources said Verizon is confident it can raise about $50 billion of bank financing to fund a deal. Market demand for investment-grade debt is proving almost limitless in the current environment, and Verizon could expect a warm welcome from investors, even with a fund-raising as big as $50 billion, bankers told Reuters.

"This is a good time for both sides to think seriously about a transaction. Vodafone's probably never going to get a better multiple than now," New Street analyst Jonathan Chaplin said. "The growth rate (for Verizon Wireless) probably has to slow over time, particularly as Sprint and T-Mobile USA and AT&T improve."

Several challenges remain, however.

Analysts and Vodafone investors said the roughly $100 billion figure contemplated by Verizon was too low and likely more of an opening gambit to bring the British firm to the table. Most analysts had put the value of the Vodafone holding at nearer $120 billion.

One top-40 Vodafone investor, speaking on condition of anonymity, said there was "absolutely no way" it will be $100 billion, but that $135 billion would suffice.

TAX STRUCTURE

A key obstacle to a deal so far has been the expectation that Vodafone could incur a hefty tax bill of around $20 billion if it sells its holding, meaning Verizon would have to pay up to make it worthwhile for the British company.

But the sources who spoke to Reuters late on Wednesday said any deal would be structured such that the eventual tax bill would likely be $5 billion or less.

Under the deal structure, Verizon would buy Vodafone's U.S. holding company, which owns the British group's Verizon Wireless interest as well as some other assets in countries such as Germany and Spain, the sources said. This structure would allow Verizon to take advantage of a provision in British tax law called substantial shareholder exemption, they said.

Chaplin said the tax bill estimate of $5 billion was consistent with his calculations.

Vodafone Chief Executive Vittorio Colao has said he has an open mind on whether to sell the group's 45 percent stake, which has come to make up around 75 percent of the firm's value in recent years as its core European business suffered.

Analysts have said a sale of Verizon Wireless would enable Vodafone to return cash to shareholders, purchase fixed-line assets in Europe, or potentially make the company an attractive takeover target for other telecom giants such as AT&T Inc.

One of Vodafone's 15 largest investors said the company should look to return to shareholders a large portion of the proceeds from a sale, while retaining a small amount to reduce debt and fund bolt-on deals.

Shares in Vodafone have risen 26 percent this year on speculation that it could finally be ready to sell its stake.

Verizon's board is expected to discuss details of a potential Verizon Wireless buyout next week at a regularly scheduled meeting being held ahead of the company's annual shareholder meeting, one of the sources said.

Taking full ownership of Verizon Wireless would give Verizon, which is reliant on the unit for growth, a lot more flexibility with the cash generated from the wireless business.

In a research note, Chaplin said a deal at $100 billion would boost Verizon's earnings per share in 2014 by 33 percent.

Verizon's shares have risen about 20 percent this year as Verizon Wireless has been easily outperforming its smaller rivals in terms of profitability and customer growth, and on rising hopes of a buyout.

TELECOM DEALS

Any deal now, if it were to happen, would come at a time when the telecommunications industry is undergoing a fresh round of consolidation. MetroPCS Communications Inc shareholders voted Wednesday to approve a merger with T-Mobile USA, a unit of Deutsche Telekom AG.

An attempt by Deutsche Telekom to sell T-Mobile to AT&T for $39 billion in 2011 was blocked by U.S. antitrust regulators. Verizon would be unlikely to face any such obstacles in a Verizon Wireless buyout.

Meanwhile, Dish Network Corp, the No. 2 U.S. satellite TV provider, last week offered to buy wireless service provider Sprint Nextel Corp for $25.5 billion in cash and stock, challenging a proposed deal between Sprint and Japan's SoftBank Corp.

(Reporting By Soyoung Kim and Sinead Carew in New York, Kate Holton, Sinead Cruise and Chris Vellacott in London and Ross Kerber in Boston; Editing by Paritosh Bansal, Martin Howell, Will Waterman and John Wallace)

By Soyoung Kim and Kate Holton