Giuliano Mignini, the lead prosecutor in Knox's murder trial, said she has been notified the investigation is over, the Daily Mail reported. The next step would be a formal charge.
Knox, a University of Washington student, was sentenced to 26 years in prison for killing Meredith Kerchner, a Leeds University student from Surrey near London. The two young women were sharing a house while spending a year studying in Perugia.
During the trial, Knox said two police officers hit her while they were questioning her. She was unable to identify the alleged assailants.
"There was no proof to back up her allegation and to protect the good name of the police department a slander investigation was started and this has now been complete," Mignini said.
Knox's parents, Curt Knox and Edda Mellas, could face slander charges for telling a British newspaper their daughter was a victim of police brutality.
Police said Knox and her then-boyfriend, who was also found guilty, killed Kerchner during a drug-fueled sex game.