Last month, Qatar Airways expressed intent to acquire about a 10 percent stake in American Airlines. On Friday, Parker said Qatar Airways needs to receive government approval for its plan and he has not heard any updates. Qatar Airways refiled its request, Parker said, leading him to believe it still has not been approved.
Earlier this month, American announced it was canceling code-share agreements with Qatar Airways and Etihad Airways because they were allegedly receiving "illegal" government subsidies. Those deals allow airlines to book passengers on each other's flights. Both airlines deny they are subsidized.
"It's not fair, and our job is to make sure that we point out that it's not fair and do everything we can to stop them from being able to expand into our markets and take away American jobs," Parker said.
The code-share agreements were helpful to customers, but they were not helpful to American Airlines, Parker said. The airlines are competing against American and other U.S. airlines "in an unfair way, and it shouldn't be allowed," he said.
American's decision to cancel the agreements has not derailed Qatar Airways' plan to buy a stake in American.
"We'll see where this all ends up," Parker said.
American Airlines posted second-quarter earnings Friday morning that beat Wall Street's expectations. Shares of American Airlines were recently down nearly 2 percent after initially rising 2 percent immediately following the announcement.
"We thought we were undervalued yesterday," Parker said. "So now we feel really undervalued over the last couple days because the market seems to be reacting to short-term revenue issues as opposed to long-term cash flows."