What will Texas International Airlines do with all its money?

That is the $46 million question being asked these days both on Wall Street and within the nation's airline industry.

Ever since the Houston-based airline agreed to sell its 25 percent share of National Airlines to Pan American World Airways for $108 million, there has been a lot of talk about what TIA will do with its money.

TIA will make about $46 million in pre-tax profits from the National stock it originally acquired in an effort to take over the Miami airline. But now, Pan Am is considered to have won the takeover battle, leaving TIA with plenty of cash to spend.

"Nobody knows and they (TIA) are not saying," one airline executive says of Texas International plans. "I bet they are probably studying something right now and have been. Because they have known the National thing has been a lost cause for some time, they knew they would end up with a lot of cash or no merger."

And like that airline official says, TIA is not discussing its plans. In fact, officials at the Houston carrier refused to make comments on any speculation or rumor currently being passed around the airline industry or on Wall Street.

"Our general posture is that when and if we have something to announce we will do it and in the meantime we will not discuss or respond to rumors on the street," says Jim O'Donnell, vice president of marketing for TIA.

But whether TIA is talking or not, there are numerous opportunities story continuing available for the airline to invest its profit.

One possibility mentioned by airline analysts would be for the carriers to pay off all its debts. "That would leave them with a very clean company," notes Mike Derchin, an airline analyst with Oppenheimer and Co. of New York. But Derchin adds that this conservative approach is unlikely for TIA, which has publicly stated its desires to grow rapidly and was referred to as "the little fish eating the big fish" when it announced plans last year to take over National.

Another approach for the carrier might be to diversify into another segment of the travel industry. Hotels, restaurants and auto rentals are mentioned as just a few of many possibilities.

Such diversification has proved profitable for other carriers. For instance, Pan Am's Intercontinental Hotel subsidiary has launched an aggressive effort to buy hotels and recently purchased the Barclay in New York City.

But while TIA's $46 million profit may seem large, it would probably be enough to buy only one or two large hotels and would provide a limited amount of capital for establishing or buying a restaurant chain or auto rental company.

M reover, airling industry observers and Wall Street analysts say such an investment by TIA would be out of character for the carrier. TIA has established itself as an aggressive airline whose main thrust has been in expanding its route system. Just last month, TIA announced a $39 million expansion of its facilities at the Dallas-Ft. Worth Airport and indicated it would spend $200 million to add 28 McDonnell-Douglas DC9 aircraft to its jet fleet over the next two years.

"What they really want to do is build their airline into a mini-trunk airline," Derchin said. "They want to be what Braniff was about five years ago. With their operating hubs in Houston and Dallas they seem to be heading in this direction."

TIA could choose to expand in two different ways.

First, the airline could create the effect of a merger by using their proceeds from the stock sale to buy aircraft and other equipment. And with the liberalized market entry rules now in effect, airlines can apply for and receive new operating authority in a relatively short time.

"They could just ask the board for any route structure they want," Derchin says, "all you have to do is ask for a route and in about two months you can get it. They could just simply use the cash to buy a lot more equipment and could apply for the routes they want."

But because many airlines are buying new jets, there is a shortage of available aircraft. Moreover, aerospace manufacturers have a large backlog of orders which translates into long waiting lines. The delivery time on a DC9, the mainstay of TIA's fleet, is about 18 months.

The remaining option, of course, is to attempt a takeover or merger with another airline.

Since TIA sold its shares of National stock to Pan Am, it has been rumored widely that Continental Airlines of Los Angeles would be Texas International's next takeover target. Speculation sent trading in Continental stock through the roof as the price of a share jumped from 8 5/8 on July 20 to 13 5/8 on July 28.

But Continental, which recently was turned down by the Civil Aeronautics Board in its effort to merge with Western Airlines, says it has had no discussions with TIA about a merger and many airline analysts say such a combination would not make any sense. While Continental would have much to offer TIA with its vast route system throughout the West extending east and through the Southwest in addition to many points in the Pacific, TIA has little to offer Continental.

But whether TIA decides to buy hotels, aircraft or another airline, almost all industry experts agree the Houston carrier's president, Francisco A. Lorenzo, won't remain idle. Said one analyst: "He has no intention to lie around stagnant."