Koroma is invited to report to the headquarters of the Criminal Investigations Department in Freetown within 24 hours, the statement said.
In response, the former president said he would honor the invitation.
"I maintain an open mind and stand ready to support the police investigations to the fullest. Let the rule of law reign supreme in our democracy," Koroma said in a statement, calling on the public to remain calm.
Gunmen attacked a military barracks, a prison and other locations in Sierra Leone last month, freeing about 2,200 inmates and killing more than 20 people in what the authorities said afterwards was an attempt to overthrow the government.
The government said the failed coup was led mostly by Koroma's bodyguards.
The former president condemned the attacks in a statement shortly after the incident happened.
Sierra Leone's information minister says 71 people have been arrested in the context of the ongoing investigation, including 45 serving military officers, seven serving police officers and 13 civilians.