The investigators also asked Smollett to ask additional questions about the attack that he reported on January 29th. Smollett's lawyers have not indicated when their client would be available to speak to the police.
Smollett told the authorities that two men had attacked him, passing a rope around his neck and spilling an unknown chemical.
Smollett denies playing a role in his attack, according to a statement by his lawyers.
In a statement, 20th Century Fox Television, which produces the "Empire" series featuring Smollett, and Fox Entertainment voiced their support for the actor on Wednesday.
"Jussie Smollett continues to be an accomplished professional on set and, as we said before, he has not stepped out of the series," the statement said.
Two law enforcement officials familiar with the investigation told CNN that the police thought Smollett had paid for two brothers to orchestrate it.
The two brothers, who were arrested and released as part of the attack, met police and prosecutors in a Chicago courthouse Tuesday, said Chicago police spokesman Tom Ahern. . The county's chief attorney, Cook County attorney Kim Foxx, is recused from the investigation, according to a spokeswoman for his office.