Speaking to reporters on Friday, Alderson said he doesn't see a scenario in which Tebow is called up from the minors.
"Never crossed my mind until about 10 days ago when somebody said it was likely to happen," said Alderson, via ESPN.com. "I don't foresee that kind of scenario."
In 80 minor league games this season, Tebow is hitting just .240/.332/.376 with 78 strikeouts in 263 at-bats.
He has fared better in 16 games since being promoted to High-A St. Lucie, posting a .327/.421/.551 slash line with three home runs in 49 at-bats. The former Heisman-winning quarterback hit a walk-off home run in Thursday's game against Daytona.
This is Tebow's first full season in professional baseball. He signed with the Mets last September and has yet to play any games above High-A.