NEW YORK, March 6 (Reuters) - Delta Air Lines (DAL), the No. 3 U.S. carrier, and Korean Air Lines (03490) plan to file as early as next week for U.S. antitrust immunity to deepen their alliance, a source familiar with the situation said. Atlanta-based Delta and the South Korean flagship carrier are partners in the SkyTeam alliance, but cementing their ties with antitrust immunity would allow them to operate as one carrier by sharing revenues, scheduling and pricing. The two carriers have a code-sharing agreement which will cover service to seven U.S. cites and flights to Seoul, Pusan, Tokyo and Osaka from May. Delta hopes to ramp up its service in Asia by taking advantage of the growth potential at Seoul's new Incheon airport and its proximity to the Japanese and Chinese markets. SkyTeam partners Delta and Air France (AIRF) last month said they would reinstate their code-share agreements with Korean Air, about three years after they were halted because the South Korean carrier was involved in a series of crashes. The U.S. Federal Aviation Authority restored Korea's air safety rating, based on International Civil Aviation Organization safety standards, to category 1 in December. Delta Air Line shares fell 37 cents to $36.54 in late-afternoon trading on the New York Stock Exchange.