American Express Corp. is exploring the possible sale of its share in the money-losing Warner Amex Cable Communications Inc., the corporation's cable television systems joint venture with Warner Communications Inc., according to both company officals and published reports.

However, Warner Communications Inc., an equal partner in the company, says it remains committed to the venture. "We've always been a great believer in the cable business and continue to be," said Geoffrey Holmes, a Warner spokesman.

Warner has the right of first refusal should American Express find a buyer for its share of the cable company. A move to sell would trigger a decision by Warner on whether to remain a significant player in the cable marketplace. Sources close to Warner indicate that it probably would not buy out American Express's portion of the joint venture.

The sale would effectively mark the end of a costly and ambitious program by both companies to diversify into cable. American Express had hoped to use cable television as an electronic delivery system for its array of financial services; Warner viewed cable as a new distribution channel for its movies and television programs. The company has lost money for nearly a decade.

"We're seeing it more as an investment than as a line operation," said Walter Montgomery, American Express corporate vice president for public affairs. "We obviously think this is a very valuable property. We're keeping our options open."

However, he added that one of the less likely options would be for American Express to purchase Warner's share of the venture as a long-term investment. "That is not an option to which this company would lean," he said.

While Montgomery said that no immediate action was pending, a source who asked not to be named indicated that a decision to sell might come as soon as the end of the month.

Higher than expected construction costs in large franchise cities such as Pittsburgh, Houston, Dallas and Cincinnati have submerged the cable venture in tens of millions of dollars in losses.

Drew Lewis, then secretary of Transportation, was hired in 1983 to turn the troubled company around. In the past two years, he has significantly cut overhead, renegotiated several costly franchise agreements and sold off systems. The Pittsburgh franchise was sold last year for $93 million. The company says it is close to the sale of its Dallas franchise. Warner Amex now says it expects to break even or be marginally profitable by the end of the year.

Though he would not comment on the report, Lewis is mentioned as a leading candidate to purchase his company in a leveraged buyout. TeleCommunications Inc. and Time Inc.'s ATC, two of the largest cable system operators, also are mentioned as possible acquirers of Warner-Amex franchises.

With roughly 1.2 million subscribers, Warner-Amex is valued by some analysts at more than $1 billion. But the company's half-a-billion-dollar debt probably would place the purchase price somewhere between $700 million and $800 million, according to Donaldson, Lufkin and Jenrette analyst Dennis Liebowitz. At that price, it would cost Warner between $350 million and $400 million to totally own the cable venture.

Warner Amex also owns the cable system in Reston, Va. Fairfax County and Media General Cable, the cable system authorized to provide cable service in the county, have sued Warner Amex, charging that its Reston operation is illegally providing cable service because it is not formally authorized by the county.