Zynga Inc., the biggest maker of games on Facebook, may file for an initial public offering by the end of June to capitalize on investors’ demand for shares of social-media startups, a person familiar with the plans said.

Zynga has met with representatives of Morgan Stanley and Goldman Sachs Group Inc. and is close to choosing bankers to help it prepare regulatory filings, said the person, who asked not to be identified because the deliberations are private.

Internet companies are lining up for IPOs after shares of LinkedIn Corp., the largest professional-networking site, more than doubled in their debut last week and Yandex NV, Russia’s most popular Web-search provider, surged 55 percent yesterday. Pent-up demand for companies that have pioneered social media and foreign Internet markets is outweighing some investors’ concern that technology shares may be overvalued.

“I think every private company watched the LinkedIn IPO and said, ‘What if I could do that tomorrow?’” Bing Gordon, a partner at venture capital firm Kleiner Perkins Caufield & Byers, said in an interview with Bloomberg Television. “But every day is different.”

Gordon, who is a Zynga board member, declined to comment specifically on the company’s IPO plans.

Music-streaming service Pandora Media Inc. is already on file to go public, as is HomeAway Inc., an online vacation- rental site. Cloudary Corp., a Chinese Internet company, announced plans yesterday for its U.S. IPO.

Dani Dudeck, a spokeswoman for San Francisco-based Zynga, declined to comment, as did Andrea Rachman, a spokeswoman for Goldman Sachs. Pen Pendleton, a spokesman for Morgan Stanley, also declined to comment. Both banks are based in New York.

Bigger Than EA

Zynga is already the second-most valuable U.S. game company, after Activision Blizzard Inc., based on trading in markets that match buyers and sellers of privately held companies. Zynga has an $8.2 billion valuation on SharesPost Inc., an exchange for private companies. That tops Electronic Arts Inc., which is valued at $7.71 billion on that Nasdaq Stock Market. Zynga hired former Electronic Arts Chief Operating Officer John Schappert for a senior role last month.

Zynga has 247.8 million monthly active users on Facebook, more than six times that of the second-leading developer, according to researcher AppData.com. The company owns three of the four most popular apps on the site -- “CityVille,” “FarmVille” and “Texas HoldEm Poker.”

Virtual Business Model

Games are free to play, and the company makes money by selling digital  — or virtual — goods within the apps and letting players pay to reach higher levels. The worldwide virtual-goods market is expected to more than double to $20.3 billion in 2014, from $9.28 billion last year, according to ThinkEquity LLC, a San Francisco-based research firm.

Zynga is backed by venture firms Foundry Group, Union Square Ventures, Kleiner Perkins, Institutional Venture Partners and Andreessen Horowitz. Russia’s Digital Sky Technologies and Google Inc. are also stakeholders. In February, Zynga was in talks to raise funding at a valuation of about $10 billion from T. Rowe Price Group Inc. and Fidelity Investments, two people familiar with the matter said at the time.

Morgan Stanley led LinkedIn’s offering, along with Bank of America Corp. and JPMorgan Chase & Co. The bank may also be chosen — with Goldman Sachs — to lead Groupon Inc.’s IPO, a person familiar with the matter said last month.

The technology blog AllThingsDigital reported yesterday that Zynga was close to filing for an IPO.