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Microsoft is in advanced talks to acquire the maker of the game Minecraft for more than $2 billion, people briefed on the discussions said on Tuesday. The move was intended to ensure that one of the most popular games was available for the computing giant’s family of devices.

The sides still need to work out many details, and a deal could fall through, according to one of these people, who spoke on condition of anonymity.

Acquiring Minecraft would give Microsoft control of an online world that has defied many of the conventions of the modern games business to become a blockbuster success.

Minecraft’s blocky graphics are crude by today’s standards, looking like virtual Lego bricks. But unlike many of the start-ups purchased by big technology companies for billions of dollars, Minecraft is already a lucrative business. This year, Mojang, the privately held Swedish company that makes Minecraft, told The Wall Street Journal that its revenue was about $360 million last year, up 38 percent from the year before. The Journal reported the discussions with Microsoft earlier on Tuesday. Mojang was co-founded by Markus Persson, a 35-year-old programmer and game designer who is better known in the gaming world by his gamer name, Notch. Mr. Persson has said in the past that he did not want to sell the company or take money from outside investors.

In an era when many games, especially for mobile devices, are given away, and derive their profit from the sale of virtual currency and other items, Mojang sells Minecraft the old-fashioned way — by charging people to buy a copy. The price varies depending on what kind of device people use to play the game, ranging from $7 on mobile phones to $27 for computer versions. A version of Minecraft for Microsoft’s Xbox, which has been a top seller for the console, costs $20.

For Microsoft, the interest in a deal is motivated in large part by a desire to ensure that attractive content is available for some of its most important platforms. Minecraft is not currently available on Windows Phone, the mobile operating system that Microsoft has struggled to turn into a strong competitor to Apple’s iPhone and Google’s Android.

Minecraft has also not been adapted to take advantage of the graphical interface of Microsoft’s latest operating system for computers and tablets, Windows 8. The game is not available for purchase in the Windows Store, Microsoft’s online app store.

Gaming remains one of the most popular applications for mobile devices and computers. The lack of timely versions of top titles for its devices has been a problem for Microsoft as it tries to compete more aggressively with rivals like Apple, Samsung and Google.

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By the standards of Microsoft, which had nearly $86 billion in cash and short-term investments at the end of June, a $2 billion-plus deal would be relatively small. Because Mojang is a European company, Microsoft would be able to use cash from overseas operations to fund the deal, a more attractive prospect than bringing the cash back to the United States where it would be subject to hefty repatriation taxes.

A spokeswoman for Microsoft declined to comment. Mr. Persson did not respond to a request for comment.

Microsoft first approached Mojang about three months ago, interested in pursuing a deal, one of the people briefed on the discussions said. By that point, the company — and Mr. Persson in particular — had considered a sale, having received takeover approaches worth about $1 billion in the last few years.

Soon after, Microsoft made an initial offer, prompting more serious talks between the sides. Last month, Mojang hired additional advisers to assist in the discussions.

Talks are continuing between them, and an agreement could be reached by the end of the month, the person briefed on the discussions said.

While Mr. Persson is said to accept that he may not stay for more than six months if a deal is struck, Mojang is pressing to try to ensure that Microsoft retains its younger developers.

In a Q. and A. hosted on the Internet forum Reddit a year ago, Mr. Persson described growing up relatively poor. After he created the popular game, he wrote, he has earned a huge amount of money that he spends on computers, gaming consoles and traveling. “I might eventually get a driver’s license so I can buy a car,” he added.