Anheuser-Busch InBev is nearing a deal to buy the half of Grupo Modelo it does not already own, according to people briefed on the matter, giving the global brewing giant control over the maker of Corona Extra beer.

A deal could cost Anheuser-Busch InBev more than $12 billion, given Modelo’s stock market value of roughly $23 billion. A transaction could be announced as soon as this week, some of these people said, though they cautioned that talks were continuing and could falter.

Negotiations between Anheuser-Busch InBev and Modelo, which is controlled by descendants of the company’s founders, have been difficult at times, one of these people said. Among the issues discussed were price and antitrust clearance.

Should the two sides reach an agreement, it would combine Modelo’s beers with Anheuser-Busch InBev’s huge stable of brands, which includes Budweiser and Stella Artois. The larger company inherited its current 50 percent noncontrolling stake from Anheuser-Busch, which InBev took over in 2008 to become the world’s biggest brewer.

It would also continue a wave of consolidation that has rippled through the beverage industry for years, one that analysts have said could eventually include an Anheuser-Busch InBev takeover of Modelo. Anheuser had held a stake in the Mexican brewer for some time, and Modelo had long been the importer of Budweiser in Mexico.

If completed, the deal would be the second-biggest takeover Anheuser-Busch InBev has ever made, trailing only the 2008 deal. It would also be a prominent large deal at a time when merger activity has slowed, as concern about the global economy has sapped corporate confidence.

But relations between the two beer makers have often been rocky. The Mexican brewer went to court shortly after the 2008 Anheuser takeover, claiming that the deal violated its pact with the Budweiser maker. An arbitrator ruled in favor of Anheuser-Busch InBev in 2010, renewing speculation about an eventual Modelo takeover.

A spokeswoman for Anheuser-Busch InBev declined to comment. A representative for Modelo was not immediately available for comment.

News of the deal’s progress was first reported by The Wall Street Journal on Sunday.