This story was shared by Time Extension and comes from former Konami VP Christopher Bergstresser. According to him, riding the wave of the first "Matrix" film's success, Andy and Larry Wachowski personally approached the Japanese company with a proposal to create a game based on their movie. At one point, they even flew to Konami's headquarters to meet face-to-face with Kojima, who had already made a name for himself with "Metal Gear Solid".
Source:
imdb
Still, Kojima himself was apparently interested in the offer, and many Konami employees were disappointed by management's decision. The zoomboola.com editorial team would like to add that after this, the rights to adapt "The Matrix" into a game went to Shiny Entertainment, which later released "Enter the Matrix" and "The Matrix: Path of Neo".