American Airlines would keep four gates at Lambert-St. Louis International Airport but shed $2.3 million a year in payments to the airport under a proposed deal with the city, the St. Louis Post-Dispatch reported yesterday. The agreement is expected to be filed next month with the U.S. Bankruptcy Court in New York, where American’s parent, AMR Corp., filed for bankruptcy protection in November 2011. Among the airlines at Lambert, American ranks No. 2 in flights, behind Southwest Airlines, with 30 departures a day to six destinations. The carrier has agreed to pay Lambert $722,811 in debt from before the bankruptcy filing and other pending amounts that are still due the airport, officials said. Airport officials were unable to estimate how much American will pay before and after approval of the settlement, but under the agreement, American has agreed to pay about 40 percent of its $542,072 annual share of terminal improvements. Lambert officials plan to file a claim in bankruptcy court for the remaining 60 percent. AMR has requested that the bankruptcy court extend the deadline for its reorganization plan until March 11.