There was no immediate comment from the American Institute. Taiwan's Defense Ministry denied the report.
Speaking to military officers in Taipei, Ma acknowledged difficulties in securing the American warplanes, which Taiwan says it needs to help defend against a possible attack from China.
"Some of our defense procurement projects from the United States including the F-16s ... are not going smoothly," Ma said. "But the government will continue pushing for the systems."
Taiwan has already been turned down three times since it first moved to acquire the F-16s in 2006, and Taiwanese officials have been informed by Washington that another formal denial would nix any chances it has to seal the deal.
While Taiwan's allies in the U.S. Congress and Lockheed Martin, which manufactures the plane, have been pushing hard for the sale, the State Department and the National Security Council have resisted, fearing that it would infuriate China. Beijing condemns all foreign military transactions with Taipei as interference in its internal affairs. The two sides split amid civil war in 1949, but Beijing still claims Taiwan as its territory.
During Ma's three years in office, tensions with China have fallen to their lowest level since the split more than six decades ago. Even so, Ma says, Taiwan still needs the planes. He says their acquisition would also give the democratic island the confidence it needs to improve its relationship with Beijing even further.
Aside from the F-16 C/Ds, Taiwan is also pressing Washington to provide upgrades for its rapidly aging fleet of 146 F-16 A/Bs. That request is also pending.