The Zynga Game Network, the maker of popular online video games, is moving closer to becoming the next hot Internet initial public stock offering.

The company is expected to file for an offering on Wednesday, according to people briefed on the matter.

Zynga’s offering may be the biggest yet by a social media firm. The company potentially will seek to sell as much as 10 percent of its shares for a price that will value the company at $20 billion or more, according to people briefed on the offering plans.

If the sale brings in $2 billion, it will be among the largest technology offerings since Google’s in 2004.

The filing is expected to shed light on Zynga’s business, including how much it depends upon Facebook for its revenue. The numbers should also provide some insight on the financials of Facebook, which is widely expected to file for its I.P.O. in the next 12 months.

Zynga has selected banks led by Morgan Stanley to underwrite the offering, people briefed on the matter said. The underwriting group also includes Goldman Sachs, Bank of America Merrill Lynch, Barclays Capital and JPMorgan Chase.

Representatives for Zynga and the banks declined to comment.

Like several of its peers, Zynga has pushed up the time line for its market debut: as recently as February, it was aiming for an I.P.O. early next year.

As the force behind popular online games like FarmVille and CityVille, the company makes the bulk of its revenue from the sale of virtual goods and now claims more than 215 million monthly active users. It has been profitable for several years, its founder and chief executive, Mark J. Pincus, has said.

Still, Zynga may encounter skepticism over the valuations of the newest Internet companies. Although LinkedIn, the social network for professionals, reached an intraday high of $122 on its first day of trading, the stock has since pulled back significantly. On Tuesday, shares of LinkedIn rose 12 percent, bolstered by a batch of positive analyst reports, and closed at $85.66.

When Zynga goes public, Mr. Pincus, who founded the company in 2007, and its venture capital investors will see their fortunes multiply. The group — which includes Yuri Milner’s DST Global, Kleiner Perkins Caulfield & Byers, Silver Lake Partners and Andreessen Horowitz — has sunk hundreds of millions of dollars into Zynga.

News of the impending filing was reported earlier on Tuesday by CNBC.