Southwest Airlines reiterated Thursday that Hawaii is one of the destinations it is considering for expansion while Allegiant Air, which already serves the state, said a day earlier that it is not planning to go much beyond its current level of service.

With the growth rate in visitor arrivals flattening out, state tourism officials have been looking both domestically and overseas for airlines to pick up the slack with additional air seats.

Dallas-based Southwest, which has been integrating its 2011 acquisition of AirTran Airways, said in an earnings conference call Thursday that Hawaii is one of 50 potential destinations it is exploring. Southwest first floated the idea about expanding to Hawaii in 2010 when it announced it would be adding 175-seat Boeing 737-800 aircraft to its fleet. Delivery of those planes began in 2012.

"We have work to do to fly to Hawaii, which I doubt we’ll be able to keep a secret," Southwest Chief Financial Officer Tammy Romo said. "So you’ll know when we made that commitment when we decide that. And it will take us not years from start to finish, but it will take some time to actually activate that. Hawaii is one of 50 potential destinations that we now have created. It’ll just have to compete priority-wise with other great opportunities that we have."

Southwest, the biggest domestic carrier, reported net income of $485 million in the past quarter. The carrier made its first international flights on July 1 to Aruba, the Bahamas and Jamaica, with service to Mexico and the Dominican Republic coming soon.

Las Vegas-based Allegiant, which began service to Hawaii in June 2012, at one time serviced the islands with as many as 10 routes. But Allegiant only offers two year-round routes now — Los Angeles and Las Vegas to Honolulu — and plans to put four other Honolulu-bound routes (Stockton, Calif.; Fresno, Calif.; Scottsdale/Mesa, Ariz.; and Eugene, Ore.) on seasonal hiatus in early August.

"What we are doing in Hawaii … has been productive, (but) we don’t intend to grow it much beyond where we are today," said Jude Bricker, senior vice president-planning for Allegiant, on a conference call Wednesday. "We’re satisfied with the production we are getting out of the airplane (223-seat Boeing 757) and the revenue that we’re achieving and the returns that we’re getting."

Allegiant earned $33.5 million in the April-June period, its 46th consecutive profitable quarter.