A letter from the city's legal department sent Thursday to Smollett and his attorneys said the figure covers overtime worked by more than two dozen detectives and officers who spent weeks looking into Smollett's claim. The work included reviewing video and physical evidence and conducting interviews.
Those resources, the letter said, "could have been used for other investigations."
Prosecutors infuriated Mayor Rahm Emanuel and Chicago's police chief this week when they abruptly dropped 16 felony counts that accused Smollett of making a false police report about being the target of a racist, anti-gay attack in January.
Smollett has maintained his innocence and insisted that the attack was real.
The prosecution sealed the case, but authorities still say the actor concocted the assault. Prosecutors offered no additional information Thursday during a court hearing where media attorneys argued that the public has a right to know what happened.
Trump tweeted: "FBI & DOJ to review the outrageous Jussie Smollett case in Chicago. It is an embarrassment to our Nation!"
The Justice Department sometimes brings federal cases after state prosecutors have declined to file charges, including after police shootings that the federal government believes might constitute civil rights violations. But department policy generally restricts prosecutors from bringing federal charges after state charges have been resolved, unless they can establish that the potential crime at issue is a federal one and involves "a substantial federal interest."
If Smollett fails to pay, officials could charge him with violating a city ordinance and seek fines, damages and court costs, the letter said.
A spokeswoman for Smollett attorney Patricia Brown Holmes declined to comment on the letter.
In the past, city officials have sought restitution from other people who made false reports and from businesses that pursued city contracts by seeking disadvantaged business status, said a spokesman for the legal department, Bill McCaffrey.
Investigators believe Smollett, who is black and gay, hired two brothers to stage the Jan. 29 attack in downtown Chicago and that Smollett hoped the attention would help advance his career. Police also allege that before the attack, Smollett sent a letter threatening himself to the Chicago television studio where "Empire" is shot.
The FBI, which is investigating that letter, has declined to comment.
Smollett attorney Tina Glandian said the two brothers are lying. She said Smollett had hired one brother as a personal trainer but had no idea who attacked him along a Chicago street until the brothers were later identified by police.
Smollett has repeatedly said the two masked men shouted slurs, wrapped a rope around his neck and poured a substance on him. He also told detectives that the attackers yelled that he was in "MAGA country," an apparent reference to Trump's "Make America Great Again" campaign slogan, police said.
Prosecutors initially charged Smollett with one felony count in February. A grand jury indicted him on 15 more counts earlier this month. But in a stunning reversal Tuesday, prosecutors abruptly dropped all charges, just five weeks after the allegations were filed.
In return, prosecutors said, the actor agreed to let the city keep his $10,000 in bail.
During Thursday's court hearing, prosecutors promised to notify media outlets if Smollett's lawyers tried to expunge his record. But lawyers for major news organizations, including The Associated Press, told the judge that the case has not been transparent.
"The public is entitled to know what happened and what's happening in this proceeding," media attorney Natalie Spears argued.
Judge LeRoy Martin said court proceedings had followed the law and that there was "no nefariousness."
In an interview with Chicago television station WGN, Cook County State's Attorney Kim Foxx said Wednesday that the law allows Smollett to have his police records sealed, but that the court files "should never have been sealed." She said she believes it was done in error but "that should not have happened."
If the case had gone to trial, Foxx said, Smollett never would have received a prison term because the 16 charges were the lowest possible form of felony. And if he pleaded guilty, it would have been to one count, not 16.
"For all of the noise and all of the media attention, it's a step up from a misdemeanor," Foxx said. Most comparable cases are resolved with probation or an agreement such as Smollett's if the defendants "don't' have a long rap sheet or a violence in their background."
Foxx recused herself before Smollett was charged because she had discussed the case with a Smollett family member. The case was then handed to First Assistant State's Attorney Joseph Magats.
On Wednesday, the ex-chief of staff for former first lady Michelle Obama said she approached Foxx regarding the case on behalf of the actor's family. Tina Tchen released a statement saying she's a friend of Smollett's family and knows Foxx "from prior work together."
Tchen said her "sole activity" was to put the prosecutor in touch with "an alleged victim's family." Tchen said the Smollett family "had concerns about how the investigation was being characterized in public."
Email and text messages that Foxx's office provided to the Chicago Sun-Times show Tchen contacted Foxx to set up a telephone conversation with the Smollett relative. Foxx told the Sun-Times the relative expressed concerns over leaked information.
Foxx told the Chicago Tribune that she regretted dealing with the relative in the investigation's early phases.
Associated Press writers Caryn Rousseau in Chicago and Eric Tucker in Washington contributed to this report.
Check out the AP's complete coverage of the Jussie Smollett case.