The software giant is said to be assembling a bid that would value the company at around $2 billion.
Originally released for PCs in 2009, Minecraft has gone on to launch on virtually every platform, selling more than 54 million copies on desktop computers, mobile environments like Android and Apple's iOS, and on consoles such as Sony's PlayStation and Microsoft's own Xbox.
It's currently the No. 1 most downloaded paid app on both Apple and Google devices.
Known as a "sandbox" game because it allows for free play as opposed to scripted, goal-based gameplay, Minecraft is essentially a virtual world in which users interact and create new environments by building and destroying blocks.
Wildly popular game
Mojang has historically been known as a counter-cultural game-maker, loath to ally itself with some of the more mainstream titans of the industry. Reaction from Minecraft's millions of players worldwide has been skeptical, but experts suggest Microsoft is unlikely to change the game in any material way, much less limit it to certain platforms.
Forty per cent of players now participate in the game on a mobile device, Nomura analyst Rick Sherlund said in a research note discussing the possible deal, so the move is likely just an attempt for Microsoft to strengthen itself in the mobile space, rather than an attempt to force gamers to buy an Xbox.
"We don't view this acquisition as a sign of Microsoft's intention to double down on Xbox, but consider it an attempt to better address mobile on a cross-platform basis," Sherlund said.
"This also appears to be consistent with CEO Satya Nadella’s mobile and cloud strategy, as he has stated that 'the single biggest digital life category, measured in both time and money spent, in a mobile-first world is gaming'," he said.
The game likely also has extensive potential for more revenues from things like toys, movies and books — some deals for which are already in place, including with Lego.
Professor Mark Skilton of England's Warwick School of Business says he sees why Microsoft would be interested in the company. Last month, Amazon bought Twitch, a website where users pay to watch other people play video games similar to sporting events, for $1 billion.
Big deals like that are going to become commonplace as moneyed tech companies are keenly aware of the amount of money being spent in the gaming space.
"The online gaming industry is fast moving from niche collective enthusiast to mass market, and Minecraft is a logical move as big business follows the traffic numbers in the digital world." Skilton said.