Qatar Airways is attempting to buy a 10% stake in American Airlines, according to a securities filing.
American Airlines said that the state-owned Qatari carrier had disclosed that it planned to buy at least $808m (£638m) in shares.
The US airline said: “The proposed investment by Qatar Airways was not solicited by American Airlines and would in no way change the company’s board composition, governance, management or strategic direction.”
Chief executive Doug Parker said in a memo to employees: “We aren’t particularly excited about Qatar’s outreach.”
The two airlines have had their differences in recent months.
American, along with United and Delta, have accused the Middle East’s largest airlines – Qatar, Emirates and Etihad – of having an unfair advantage through government ownership and subsidies.
Mr Parker said Qatar’s move with this in mind was “puzzling”.
The Middle East airlines have also moved into overseas routes that had previously been important to their US competitors.
The Qatar stake in American “does not alter American Airlines’ conviction on the need to enforce the Open Skies agreements with the United Arab Emirates and the nation of Qatar and ensure fair competition with Gulf carriers, including Qatar Airways,” American Airlines said in the filing.
“American Airlines continues to believe that the President and his administration will stand up to foreign governments to end massive carrier subsidies that threaten the US aviation industry and that threaten American jobs.”
Under US law, foreign ownership in airlines is restricted to 25%.
For passengers in the US, any deal could make it easier to travel, especially to smaller cities in India and parts of Asia. The two airlines are already members of the Oneworld group, which means passengers can earn and use points on both airlines.
Shares in American Airlines rose 2.9% in early trading.
The news comes after Saudi Arabia, Bahrain, Egypt and the UAE cut ties with Qatar over alleged support for extremist groups, something the Qatari government denies. The countries have suspended flights to and from Qatar.