Mayor Brandon Johnson said as many as 22 busloads of asylum seekers could arrive in Chicago Wednesday.
Currently, more than 9,800 migrants are being housed in city shelters.
More than 3,000 others are at police stations and airports, awaiting placement.
Chicago has received more than 17,000 migrants since the mission began.
Johnson on Wednesday confirmed that a team from Chicago will visit operations at the border, and that a Homeland Security team arrived to assess the migrant situation in Chicago.
In Streeterville, there are growing complaints about issues community members are linking to the shelter.
For over a year, the Inn of Chicago on the corner of East Ohio and St. Claire streets has housed over 1,500 new arrivals.
"We've been co-locating young migrant families with hundreds of young adults in the same facility, and we are seeing it play out in a horrible way," 42nd Ward Ald. Brendan Reilly said.
"We had over 300 911 calls for service this year alone, a majority for things like fighting disturbance, narcotic sales; so, it's a real problem for the community," 2nd Ward Ald. Brian Hopkins said.
Both aldermen say the trouble is being caused by young single migrant males, not the families. They're calling on the Johnson administration to not renew the contract with the hotel when it expires at the end of the year.
"It has actually been a very lucrative deal for the owner of this facility. I would imagine he would like to continue to because he is being paid for full occupancy, and the hotel was rarely occupied fully," Hopkins said.
Residents and some businesses say they have had enough.
"I can go to my 15th floor and hear noises starting at 7, 8, 9 non-stop for hours," resident Victor Zusman said.
Neighbors say at night there are close to 200 people on the sidewalks, causing disturbances to a neighborhood that was known to be quiet.
Reilly and Hopkins said they have made repeated requests to the city for more security, inspections and services. The aldermen say the situation is also affecting tourism: The Inn is located right off of Michigan Avenue.
"The city is clearly not equipped, and cannot afford this continued flow of migrants," Reilly said.
While they want the shelter to shut down, Reilly and Hopkins have not offered any alternative sites for the 1,500 migrants living there.
The Johnson administration has not responded to questions about whether the contract will be renewed with the Inn of Chicago.