They said the neighborhood is already dealing with a lack of resources.
"We are struggling right now to make Woodlawn an affordable mixed-income community. While I would love to help immigrants and everybody else, I would like to help my own first," Woodlawn resident Jeane Clark said.
"We are not anti-immigrant, we pro-Woodlawn," fellow Woodlawn resident Jennifer Maddox said.
Maddox is challenging Alderwoman Jeanette Taylor in the 20th Ward race.
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Taylor claims she wasn't include in the initial discussions about housing the asylum-seekers at the former Wadsworth Elementary School building at 64th and University.
"So literally you are making decisions about a building in my community without the person that was elected to represent the people," she said.
But Taylor said she was notified Wednesday by city officials that the plans to move the migrants into the building have been put on hold while they gather community input.
"So that's been my issue, you don't impose things on us. You wouldn't do this in Lincoln Park or Hyde Park," Taylor said.
Carlas Prince Gilbert is a Woodlawn business owner and resident. She said she wants to know how housing migrants could impact the neighborhood.
"What is the plan to integrate them to the community," she said.
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Little Village Community Council President Baltazar Enriquez said he understands the concerns of Woodlawn residents.
He believes the asylum-seekers would be better served near people who understand their culture and language.
"Our community is a welcoming community for immigrants. This is one of the largest Mexican American community, so we know how it feels. Our team is ready," Enriquez said.
Enriquez said city officials need to do a better job of reaching out to grassroots organizations like his that have been helping the migrants restart their lives in Chicago.