Heyman cites "people familiar with the situation" as saying only a good finish could save the jobs of Minaya and manager Jerry Manuel.
"I focus on doing my job today, and that's all I can control," Minaya told Heyman.
Owner Fred Wilpon had insinuated earlier this month that Minaya's job was safe.
The Mets entered Tuesday's game with Florida with a 62-62 record, better than last season's 70-92 mark, but hardly up to New York expectations.
Heyman lists Kevin Towers, John Ricco, Wayne Krivsky and Pat Gillick as potential replacements. Ricco and Krivsky are already with the Mets. He also lists Bob Melvin as the "leading candidate" to replace Manuel with Wally Backman as another possibility.
-- C. Trent RosecransFor more baseball news, rumors and analysis, follow @cbssportsmlb on Twitter or subscribe to the RSS feed .