Detectives are actively investigating the allegation, but have not confirmed it to be true, the official said.
Chicago police said this weekend that they are "eager" to re-interview Smollett after releasing the two brothers, who were initially identified as persons of interest in the alleged Jan. 29 attack in Chicago's Streeterville neighborhood.
The brothers, who are not considered suspects in the attack, also told police that they were paid to stage the attack, the official said.
RELATED: Timeline of key moments in alleged attack on 'Empire' actor
"We are not racist. We are not homophobic and we are not anti-Trump. We were born and raised in Chicago and are American citizens," the brothers said in a statement.
The actor is not slated to meet with police Monday, but his attorneys, "will keep an active dialogue going with Chicago police on his behalf," a Smollett spokeswoman said.
The FBI is investigating the letter, which was sent to the Chicago studio for "Empire."
After the police department investigated Smollett's attack for weeks as a possible hate crime, they discovered that one of the brothers bought the rope to be used in the attack at a local hardware store. The Chicago Sun-Times reports the store was the Crafty Beaver hardware store in Ravenswood.
Smollett told the police he was walking on the 300 block of East North Water Street in Streeterville about 2 a.m. on Jan. 29 when two unknown men walked up and attacked him, yelled racial and homophobic slurs, hit him in the face, poured a chemical substance on him and then put a rope around his neck.
A CPD spokesman said Sunday, "While we are not in a position to confirm, deny or comment on the validity of what's been unofficially released, there are some developments in this investigation and detectives have some follow-ups to complete which include speaking to the individual who reported the incident."
RELATED: Brothers tell police that Jussie Smollett paid them to stage attack, sources say
Last week, Smollett said in an interview with Robin Roberts on "Good Morning America" that he is pissed off and feels attacked that people even doubt the validity of his story.
WATCH: Jussie Smollett interview with "Good Morning America": 'I am not weak'
Late Saturday, Smollett's attorneys Todd S. Pugh and Victor P. Henderson released a statement, addressing reports that the actor may have staged the attack.
"As a victim of a hate crime who has cooperated with the police investigation, Jussie Smollett is angered and devastated by recent reports that the perpetrators are individuals he is familiar with. He has now been further victimized by claims attributed to these alleged perpetrators that Jussie played a role in his own attack. Nothing is further from the truth and anyone claiming otherwise is lying.
"One of these purported suspects was Jussie's personal trainer who he hired to ready him physically for a music video. It is impossible to believe that this person could have played a role in the crime against Jussie or would falsely claim Jussie's complicity.
"Jussie and his attorneys anticipate being further updated by the Chicago Police Department on the status of the investigation and will continue to cooperate. At the present time, Jussie and his attorneys have no inclination to respond to "unnamed" sources inside of the investigation, but will continue discussions through official channels."
If convicted of filing false police report, which is a felony in Illinois, Smollett could face up to three years in prison.