"[The Sphere] offers just how much horror, tragedy, violence went on that day," Battery Park resident Jeffery Mihok said.
Mihok called the current memorial "very crisp and antiseptic," and said the sculpture would provide a "great counterpoint to the thought-out nature for the rest of the memorial."
9/11 Memorial President Joe Daniels, who was at the meeting to update the board about projects and construction, said the sculpture couldn't be placed inside the hallowed grounds.
"It's just not a part of the design of the memorial plaza itself," said Daniels, who added that they are unable to add objects not part of the original plans.
The Sphere is currently slated to be moved from Battery Park to a new location, which the Port Authority of New York and New Jersey is expected to announce this week.
It was supposed to have been moved to a hangar at John F. Kennedy International Airport until a new home was found, but officials decried the plan.
"It simply cannot be mothballed in some musty hangar at JFK," Sen. Charles Schumer told reporters Saturday.
"It must remain, like now, accessible as a public touchstone for New Yorkers and the visitors from the four corners of the globe."
But community members feel there is only one acceptable place for it to move.
"Putting The Sphere anywhere else denies its meaning," said Michael Burke, whose brother was a first responder killed during the attacks.
Burke started the petition and said he has gotten signatures from people from all over the world.
"'Do the right thing,' is the most common thing expressed on the petition," he said.
Daniels said that while The Sphere can't be placed inside the memorial, he wants to help make sure it is placed somewhere appropriate.
"The most important thing is that this artifact is preserved in a way the public can visit it, learn about it any way they want to," Daniels said.