BRUSSELS/LONDON (Reuters) - Anheuser-Busch InBev SA's (>> AB INBEV) interest in buying the rest of Mexico's Grupo Modelo (>> Grupo Modelo SAB de CV) on Monday warmed investors eager to see fresh consolidation in the global beer market.

Shares of both brewing giants rose after Modelo and Belgian-based AB InBev, which has a 50.4 percent noncontrolling stake in the Mexican company, said on Monday they are discussing expanding their joint relationship.

Fueled by Mexico's growing beer market, AB InBev could unlock big cost savings and give the company control of exports of Corona beer, the No. 1 imported brand in the United States.

The deal, which would follow a series of recent mergers in the industry, could be worth well over $10 billon, though the family-controlled Mexican brewer said nothing was set in stone.

"These talks may or may not result in the consummation of a deal and any speculation on the terms and conditions is premature," Modelo said in a statement.

An agreement would give Anheuser-Busch InBev, the world's largest brewer, access to the Mexican beer market which is growing by 2 to 3 percent a year.

Mexico is the world's sixth-biggest beer market and the fourth-most profitable, and is a virtual duopoly between No. 1 player Modelo and Heineken (>> HEINEKEN).

In terms of volume, Modelo is the world's seventh-biggest brewer, according to independent researcher Plato Logic.

Market analysts said it would be a good deal for AB InBev.

"We believe a take-out price would be closer to $15 billion, equating to a 30 percent control premium in line with historic average brewing premiums," said analysts at Citi, who believe the deal could generate at least $250 million in cost savings.

Still, AB InBev must win the approval of the close-knit group of Modelo shareholders - many of whom are related to the company's founders - who control the company.

That is unlikely to come cheaply.

Modelo shares jumped 19.3 percent to close at 116.87 pesos ($8.37) on Mexico's stock exchange, which earlier suspended trading in the stock after it soared early on. That made Modelo worth about $27.2 billion at today's exchange rate.

AB InBev shares, which were also briefly suspended, closed up 2 percent at 56.75 euros ($70.82), making them the biggest gainer in the FTSEurofirst 300 index <.FTEU3> of leading European shares.

A deal would benefit AB InBev because it would give the company control of a brand that sets the price for import beers, or the high end of the beer market in the United States, wrote Consumer Edge Research analyst Brett Cooper.

So far, the plus side of AB InBev's relationship with Modelo has been limited to a stream of dividends, noted analysts at ratings agency Fitch Ratings.

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Banking sources said the two sides were in intensive talks, but the sticking point was the size of the premium the Modelo families can extract from AB InBev.

"The families are willing to sell but they want a big price as they see a big boost for AB InBev from owning 100 percent of Modelo," said one banker close to the talks.

AB InBev inherited its stake in Modelo when InBev bought Anheuser-Busch in 2008 for $52 billion, and after sharply cutting debt and reporting free cash flow of $9.1 billion in 2011, the group has scope to finance a possible deal in cash.

It would be the latest in a string of changes in the global brewing industry as companies seek growth in emerging markets and look to make big savings in procurement and distribution.

In April, AB InBev agreed to buy the Dominican Republic's Cerveceria Nacional Dominicana for more than $1.2 billion, while in the same month Molson Coors (>> Molson Coors Brewing Company) bought East European brewer StarBev for 2.65 billion euros ($3.5 billion), and last year SABMiller (>> SABMiller plc) purchased Foster's for $11.8 billion.

A deal between Mexico City-based Modelo and AB InBev could finally end what has been a rocky relationship since 2008, when Modelo launched an arbitration case claiming it was not consulted about InBev's acquisition of Anheuser-Busch.

The way was cleared for AB InBev to increase its Modelo stake when the Mexican brewer lost the case in 2010, but Modelo Chief Executive Carlos Fernandez said at the time that controlling shareholders would not sell their stake.

Shares of Constellation Brands Inc (>> Constellation Brands, Inc.), which has a joint venture with Modelo called Crown Imports, rose 12.9 percent to close at $21.86 on speculation that Modelo may buy Constellation's stake in Crown Imports after being acquired by AB InBev.

The joint venture imports and distributes Modelo's beers, including Corona, in the United States.

($1 = 13.92 Mexican pesos)

($1 = 0.8013 euros)

(Additional reporting by Elinor Comlay in Mexico City and Martinne Geller in New York; Editing by Anna Willard, Jeffrey Benkoe, Phil Berlowitz and Matthew Lewis)

By Philip Blenkinsop and David Jones