Alexandria Cablevision Co., the local firm awarded the Alexandria cable television franchise two years ago, told the City Council last night that financial difficulties will force it out of business.

Company officials said they plan to sell out or otherwise transfer the franchise to a larger firm with more capital to pour into the venture.

Alexandria's cable system is only the second in the Washington area to begin operations. The other -- in Arlington -- also experienced financial difficulties in recent months. Arlington Telecommunications Corp. was granted an early 14-year extension of its franchise last month after claiming it was threatened with bankruptcy.

Alexandria's 36-channel system currently is available to about 90 percent of the city's households, and has about 10,000 subscribers.

Officials of Alexandria Cablevision told the City Council last night that inflation, high interest rates and an inability to compete with larger cable franchises for managerial and technical talent are responsible for its predicament.

Charles Henry Smith Jr., chairman of the company's board of directors, gave the council a written statement, saying that the company has received several purchase offers that would "result in the merger of the assets and expertise of a larger company with the current resources of ACC."

The company has signed no agreement yet, and according to Alexandria's elaborate cable franchise laws, the City Council has the power to veto any purchaser. Among the 11 companies that have been considered, the three strongest contenders are the Chicago Tribune, American Cablevision of Boston, and Jones Intercable of Denver. "I understand they have cash in hand," said council member Donald Casey.

One of the potential purchasers, American Cablevision, is represented by the law firm of Sullivan and Worcester in which Alexandria Vice Mayor Robert Calhoun is a partner. Calhoun yesterday informed the city of his involvement and said he would not be voting on the matter.

Although the cable industry is considered to be extremely lucrative in the long run, industry analysts say the high cost of stringing cable to subscribers means that most companies must wait up to 10 years from the start of transmission before receiving a return on their investment.

In his statement, Board Chairman Smith said the estimated cost to build the system had grown from $3.6 million in January 1978 to $8.2 million in November 1980, and that current estimates indicate the cost might be $2 million or $3 million more. In addition, Cablevision's bank, State Street Bank and Trust Co. of Boston, is lending at 22 percent interest, while the franchise's cost projections were based on a maximum 15 percent interest.

According to Alexandria Cablevision, the growing costs of completing and operating the system have been so severe that the 40 or so local shareholders who once owned 100 percent of the company now own only 56 percent of the enterprise.

Smith said small, independent franchises face a number of problems, including a disadvantage in contracting with cable industry suppliers. For example, council member Casey said Alexandria Cablevision pays $1.50 more per subscriber to get Home Box Office (HBO) service for its customers than a larger franchise would.