Financial News Network announced yesterday that it has agreed to sell its troubled 24-hour business and sports cable channel to a joint venture of Dow Jones & Co. and Westinghouse Electric Corp.

The purchase would bring together FNN's strong cable franchise with the nation's dominant business publisher, Dow Jones, and one of the nation's premier broadcasting companies, Westinghouse.

Coincidentally, the purchase also would pit Westinghouse head-to-head in the cable business with one of its major consumer and defense electronics rivals, General Electric Co., which owns CNBC, a cable company that competes with FNN.

Before the sale can be completed, however, FNN must file for bankruptcy court reorganization because the sale price will not be sufficient to repay all of FNN's creditors and the new owners don't want to inherit those unpaid obligations, officials from FNN and Westinghouse said.

In the stronger hands of Dow Jones and Westinghouse, FNN could prove a formidable competitor. Many analysts consider Ted Turner's Cable News Network as the dominant cable business news but have long thought that FNN could mount a serious challenge to CNN if it had the proper backing.

Westinghouse, one of the country's largest broadcasting concerns with TV and radio stations around the country, and Dow Jones, publisher of the Wall Street Journal and the business news weekly Barron's, could be just the backing needed to turn FNN around.

Although its cable channel reaches about 35 million homes, FNN has been plagued over the last year by huge losses and by allegations that it has been mismanaged by its largest shareholder, Infotechnology Inc. Nonetheless, the cable property is considered to be Infotechnology's most valuable asset. Both FNN and Infotechnology are publicly traded, New York-based companies.

The proposed sale leaves unanswered the fate of Infotechnology's other major holding, Washington-based United Press International, which has been struggling for years to stay afloat. Officials at Infotechnology have hinted for months that undisclosed buyers have been considering purchasing the news service, but so far no one has stepped forward.

A spokesman for Infotechnology said that the sale to Dow Jones/Westinghouse would involve only the name FNN and FNN's cable operations. Excluded from the deal would be FNN's market data services operation and FNN's stake in the Learning Channel, a Rosslyn-based cable company. Currently, FNN and Infotechnology jointly own 51 percent of the Learning Channel.

FNN would not disclose the sale price, except to say that it would be less than FNN's liabilities, which at June 30, 1990, the latest total figures available, were $126.4 million. Recently, FNN announced it has $50 million in bank debt and $88 million in leasing obligations, which combined exceed the June 30 number.

FNN officials said in a release that the price they expect to fetch for the cable channel will be less than FNN's liabilities and that it doesn't expect other asset sales to make up the difference. The result could be that some FNN creditors will not be paid in full.

Infotechnology put the cable network on the sales block in November. At the same time, FNN said it expected to lose about $73 million in 1990.

Although the deal is not expected to become final for three months, the Dow Jones/Westinghouse venture is expected to begin operating the cable television company before then, though an FNN spokesman said an exact date has not been set.

FNN's two chief executives, Alan J. Hirschfield and Allan R. Tessler, took over the helm of the company last year with the express purpose of trying to find a buyer for FNN, for which they each will receive an undisclosed percentage of the sale price.