The Mets reportedly had talked to at least two teams about trading the former ace for a reliever.
Alderson said Tuesday that new Mets manager Mickey Callaway and pitching coach Dave Eiland told him that they want Harvey on the roster in 2018.
"The most important thing I am weighing are the opinions of Mickey Callaway and Dave Eiland, and they don't want to lose him," Alderson said. "Everything else today is moot."
Alderson wouldn't promise, however, that Harvey wouldn't be traded, telling reporters, "No one is untouchable."
Harvey, who was suspended three games last season after failing to show up for a game in May, is eligible for arbitration this winter and then free agency in the fall of 2018.
Harvey, 28, was 5-7 with a 6.70 ERA in 18 starts last season after returning from surgery for thoracic outlet syndrome that cut his 2016 season short. He made only 17 starts that season, going 4-10 with a 4.86 ERA.
He was an All-Star in 2013, when he went 9-5 with a 2.27 ERA. He also pitched well in 2015, finishing 13-8 with a 2.71 ERA.
Harvey made two starts in the 2015 World Series after missing the 2014 season following Tommy John surgery.