CBS also reported that trailers have been set up as temporary living quarters on the Army Reserve Training Center about 50 miles (80km) south-west of Chicago.
Fencing was also put up around the training facility late on Tuesday.
Local officials have said they have received few details on the troop assignments.
Trump argues the use of the troops is necessary to quell violence in Democratic-controlled cities, crack down on crime and support his deportation initiatives.
National Guard troops have limited power. They do not enforce the law, or make arrests, seizures, or searches – their role is instead about protecting federal officers and property.
Trump has already sent guard members into Los Angeles and Washington, DC, and has ordered them to enter Memphis and Portland.
A federal judge temporarily barred troops from deploying to Portland, however. Another judge has allowed the Chicago deployment for now.
Chicago has seen an increase in protests over immigration enforcement in the city, many of them happening outside US Immigration and Customs Enforcement (ICE) facilities.
Last weekend, US Border Patrol personnel shot and injured a woman after a group of people rammed cars into immigration enforcement vehicles – though local media report that her lawyer has contested parts of the government’s version of the events.
A hearing is scheduled for Thursday in the lawsuit filed by Illinois and Chicago – which are suing to stop National Guard troops from their state and from Texas being federalised, or brought under the control of the president.
Chicago Mayor Brandon Johnson told BBC News on Tuesday that doing so, “literally handpicking National Guard people from another state, the state of Texas, and then sending them to the state of Illinois – this is illegal, unconstitutional, and dangerous”.
On Monday, Johnson signed an executive order banning ICE agents from operating on city-owned properties.
The deployments have posed both legal and constitutional questions, as National Guard troops are typically deployed by a state’s governor and century-old laws limit the government’s use of the military for domestic matters.
Trump has said that he would consider invoking an even older law, the Insurrection Act, if federal courts stopped his deployment of National Guard troops to US cities.
The 1807 act allows a US president to use active-duty military personnel to perform law-enforcement duties inside the country.
Asked about that in the Oval Office on Tuesday, Trump referenced Chicago and said that “if the governor can’t do the job, we’ll do the job”.
