The offer was made in talks between the visiting Myanmar president and Malaysian Prime Minister Najib Razak in Putrajaya on March 13.
Malaysia has two airlines, Malaysia Airlines and AirAsia, which currently fly between Kuala Lumpur and Yangon.
President U Thein Sein advised the Malaysian operators to extend their routes to his country's second largest city and the old capital.
The Malaysian prime minister said it would be up to the airlines to decide, and promised to convey the message to the carriers, Malaysian Foreign Minister Anifah Aman said.
President U Thein Sein ended his first visit to Malaysia on March 13.