NEW YORK (AP) _ As American Express tries to stabilize its consumer charge card business, analysts say the company enjoys a solid footing with its other businesses: travel, consulting and financial planning.

The company's IDS Financial Services Inc., a Minnesota money management and financial planning business, continues to enjoy a strong market position and is expected to grow by an estimated 15 percent annual rate, Jeffrey Stiefler, American Express president, said in an interview. Analysts don't quibble with the projection.

Also expanding is the company's travel business, which claims a 26 percent share of the $130 billion corporate travel and entertainment market, Roger Ballou, president of American Express Travel Services Group, said in an interview.

In the last three years, American Express has acquired travel agencies with $1.2 billion in sales, but the real growth will be internationally, Ballou said. This year alone, it has purchased agencies with $1 billion in sales.

''Serving corporations through T&E (travel and entertainment) is going to be a cornerstone of our growth in the next few years,'' Ballou said. The company seeks to enhance its consulting business by offering data processing and advisory services on travel expense management. Travel expense is the third-largest expense category at many companies, behind salaries and data processing.

Ballou also is in charge of the charge cards targeted to companies for their employee's travel and business supply expenses. The company's corporate cards hold a strong position, while consumer charge cards have lost ground to bank credit cards, most analysts agree. Visa-branded cards have gained because many lack an annual fee and reward consumers with discounts for using the card regularly.

American Express expects its corporate and purchasing cards to grow quickly in coming years. Total corporate card spending grew 9.8 percent at American Express last year.

''The greatest strength is they have a lead in the corporate card area,'' concedes Peter Dimsey, president for the United States region at MasterCard International.

But MasterCard and Visa International are trying to capture a share of the $38 billion business card market.

Visa earlier this year reported strong growth in 1992 transactions in travel and entertainment: 14.3 percent for airlines, 13.6 percent in car rentals, and 7.6 percent in lodging.

The bank cards scored a victory in March when General Electric Corp. said it would drop its American Express corporate charge card account, with an estimated $700 million in annual charge volume, and have a bank owned by GE issue Visa and MasterCard-branded corporate cards, according to Credit Card News, a Chicago-based industry newsletter.

Despite these gains, there are few banks that issue corporate travel credit cards, leaving American Express dominating the market with 5.3 million cards.

American Express is confident about the growth prospects of IDS now that the company has sold its Shearson Lehman Brothers retail brokerage business. Shearson's brokers and the IDS sales force sold competing products and services. That, in turn, inhibited American Express' plans for cross-selling products among its various businesses, such as pitching IDS investment planning services to the card members.

Because of the Shearson-IDS conflict, ''we really were foreclosed on a lot of options,'' Stiefler said. ''It just created an impossible situation within which synergy could take place.''

Harvey Golub, American Express chairman and chief executive, said ''the opportunity is huge'' for cross-selling the card members with IDS.

Alison Deans, brokerage industry analyst for Smith Barney Shearson, said the charge card members are ideal potential customers for IDS and even a small amount of new business from this group would be beneficial.

Already, the IDS mutual funds are well-regarded in the industry. The IDS mutual funds land solidly in the middle of several mutual fund rankings and feature good service, high customer retention and a well-trained sales force, said Don Phillips, publisher of Morningstar Inc., the mutual fund ratings service.