Greg Hayes told the American news outlet that the Arizona-based company wanted to increase production of surface-to-air missiles to 12 a year.
Ukraine currently has two full Patriot systems at its disposal, which include a launcher, radar and a control station.
The Ukrainian military reportedly changed the settings to allow for the tracking and destruction of hypersonic missiles, which travel at twice the speed of missiles the Patriot was designed for.
The Russian Defense Ministry said in mid-May that Russian troops had destroyed a Kiev-stationed Patriot with a hypersonic Kinzhal missile. Russian Defense Minister Sergey Shoigu announced a successful hit on another Patriot two weeks later.