Zynga Inc., the social gaming company, has already raised $360 million from venture capital and investment firms, not including an undisclosed amount from Google. The company recently began raising another $250 million in a new round of funding in hopes to value the company between $7 billion and $9 billion. By publishing titles like FarmVille and CityVille, which have 96 million and 51 millions active players, respectively, the company has made $850 million in revenue, and $400 million in profit. Hiring Dave Wehner from Allen & Co. as their chief financial officer last year has increased interest from potential investors who believe the company will go public soon. Many investors wish to get a piece of the company through privately negotiated deals with current or former employes, or by investing in limited liability companies. Larry Albukerk, managing director of the San Francisco based investment firm, EB Exchange Funds, says he has gotten many requests from wealthy clients hoping to invest in Zynga even before it goes public.

Social-gaming company Zynga Inc. is holding discussions with potential investors about raising around $250 million in new funding in a deal that could value the three-year-old start-up at between $7 billion and $9 billion, according to people familiar with the matter.

In April Zynga filed papers authorizing the issuance of new stock that valued the company at about $4 billion.

The discussions are the latest sign of the investor frenzy around a small class of large, fast-growing Web start-ups focused on the consumer market that have yet to go public. Facebook Inc., Twitter Inc. and the group-buying service Groupon Inc. have all recently raised large rounds of funding at sky-high valuations, with some recent discussions concerning Twitter valuing the micro-blogging service at $8 billion to $10 billion. The business social network Linked In Corp. and Internet radio service Pandora Media Inc. recently filed to go public.

Any decision to raise a fresh round of funding by San Francisco-based Zynga, which sells virtual goods in Facebook games, could be weeks away and may not happen, said the people familiar with the matter. Although valuations of the most successful Internet start-ups are getting pricey—topped by Facebook’s eye-popping $50 billion value in its latest round of funding—part of Zynga’s appeal is that it has tapped into a lucrative method of making money online.

The company makes an addictive array of games like FarmVille and CityVille in which people spend real money to buy virtual goods, such as seeds to produce crops in FarmVille and virtual cash to construct buildings in CityVille. Using the social connections people maintain on Facebook to spread virally, City Ville and Farmville now have 96 million and 51 million active monthly players, respectively, according to AppData.com, which tracks Facebook statistics.

The huge audience for its games—Zynga has a total of 275 million active monthly users across all its titles—helped Zynga generate about $400 million in profit last year on approximately $850 million in revenue, said another person familiar with its finances. A spokeswoman for Zynga declined to comment.

The company has no immediate need for financing because it is profitable and has raised a sizable war chest already, several people familiar with the matter said. Zynga has said it has raised $360 million from a range of venture-capital and other investment firms. That figure doesn’t include an undisclosed amount from search-giant Google Inc.

Zynga is in conversations with at least one major bank about raising financing, as well as mutual funds and others, according to people familiar with the matter.

According to a person familiar with the company, Zynga has been barraged with interest from potential investors, who view the company as a likely candidate to go public within the next one to two years.

Zynga last year hired investment banker Dave Wehner from Allen & Co. as its chief financial officer in a move that was seen as readying itself for an eventual initial public offering.

One financing method Zynga will likely avoid is a “special-purpose vehicle” akin to the one Goldman Sachs Group Inc. created to allow wealthy foreign clients to invest in Facebook during the social-networking company’s recent round of financing. Goldman teamed up with Russian Internet investment firm Digital Sky Technologies to invest $500 million in Facebook in January and raised an additional $1 billion through the special-purpose vehicle.

But Goldman decided against letting U.S. clients invest in Facebook because it feared it could run afoul of certain regulations relating to private placements of stock. The episode has soured people on structuring such deals, and Zynga isn’t seriously looking at that option, according to a person familiar with the matter.

Zynga could use any new financing to help fuel its torrid acquisition pace. The company has averaged one acquisition a month for the past nine months, most of them involving smaller game developers. The company hired more than 800 people last year and now has roughly 1,500 employees.

The heat around Zynga is creating a frenzy among investors who are trying to get a piece of the company in the private-company share market, otherwise known as the secondary market. Some investors can purchase stock of private companies by investing in limited liability companies created to purchase such shares, or through deals brokered with current or former employees.

Larry Albukerk, the managing director of San Francisco-based investment firm EB Exchange Funds, has already brokered tens of millions of dollars of such deals for shares of hot private Internet start-ups such as Facebook, LinkedIn and Twitter. He finds employees who want to sell and then connects them to interested buyers, helping to negotiate the deal at an agreed-upon price.

Mr. Albukerk said he has gotten calls about Zynga lately from more than 100 wealth managers and professional investors. After Facebook, Mr. Albukerk said, Zynga is the hottest company. “Guys call me up and tell me just go out and get it,” he said. “The number of requests and activity is crazy compared to last year.”