This game is just getting started.

Electronic Arts — the force behind such popular video games as “SimCity” and “Madden NFL” — is quietly exploring a sale, The Post has learned.

While the discussions are at an early stage, the gamemaker has been approached by private-equity giants KKR and Providence Equity Partners about a potential transaction, according to sources.

“It’s early days,” said one source.

Electronic Arts said it doesn’t comment “on rumor and speculation.” Henry Kravis’s KKR declined comment, while Jonathan Nelson’s Providence did not return calls.

Providence also owns Bethesda, a leading independent gaming company.

EA, whose market cap is around $4 billion after a 37 percent drop this year, has been buying back shares. The stock closed up 3 percent, or 38 cents, yesterday at $13.09.

“They’ve made it known they’d do a deal at $20 a share,” said one source familiar with the company.

EA’s largest rival, Activision Blizzard, also explored a sale earlier this year. Although it didn’t result in a deal, Activision parent Vivendi shopped its 61 percent stake in the videogame giant, which was worth around $8 billion.

Like its rivals, 30-year-old EA has been challenged by the changes roiling the traditional gaming business. Sales of hardware consoles and software have slumped along with the rise in popularity of mobile and casual games that users can play for free online. Consumers are also buying fewer $60 games.

US sales of new videogames, consoles and accessories fell 20 percent in July, capping a string of declines that have plagued the industry since November.

In total, sales fell to $548.4 million last month, down from $686.3 million a year earlier, according to market researcher NPD Group.

“The handheld casual console market has evaporated because of tablets,” Michael Pachter, an analyst at Wedbush Securities, told The Post.

Pachter is nevertheless expecting EA’s stock price to more than double in the next 12 months.

EA and other traditional gamemakers are trying to figure out how to distribute a single title across multiple platforms, including consoles, PCs and smartphones.

“The problem is they’re in the fifth year of a three-year turnaround,” Pachter told The Post.

Along with the industry, EA was hit hard by the recession in 2008, and failed to anticipate the strength of social networks and tablets in transforming the gaming market.

The Redwood City, Calif., company is now the No. 2 player behind Zynga in social games that users play through Facebook and similar sites, according to Wedbush data.

The company’s digital revenue — driven in large part from “SimCity Social,” a Facebook game — grew to $324 million in the first quarter from $209 million in the same period a year ago.

Yesterday, EA said it would give away “Command and Conquer” free of charge to help in the digital transition.