In their reporting, Italian news outlets did not specify the source of their new information.
Italian news agency ANSA reported that Olsen's boyfriend, a fellow artist, discovered her body on Saturday after growing concerned because he had not heard from her. He asked her landlord to go with him to Olsen's apartment to check on her, according to ANSA.
Her death is being treated as a homicide, police spokeswoman Maddalena Carosi said on Italian TV.
ANSA reported that Olsen had been strangled, but authorities declined to comment on the cause of death until an autopsy is complete.
Initial results of her autopsy were expected Monday, prosecutor Giuseppe Creazzo told CNN. But toxicology and other tests could take much longer, he said.
Olsen had last been seen early Friday at a Florence nightclub, he said.
Although the boyfriend has an alibi that lines up with testimony from other witnesses, Creazzo said Monday that "no one has been excluded" and "no track has been excluded."
Authorities are also looking into pictures on Olsen's Instagram feed in which she said, "I have a stalker."
It was unclear whether the posts were serious.
Olsen was originally from Florida. She was living in Florence, where her father, an architect, works at an art school.
"The police haven't really said anything yet. My son is waiting for the police to share more," Olsen's grandmother, Ann Olsen, told CNN by phone from Florida.
CNN affiliate WJAX
in Jacksonville, Florida, spoke with Olsen's friends, who described her as infectiously happy.
"She was full of life. She never met a person who didn't like her," the station quoted Staci Kelly as saying about Olsen. "She had the best personality."
Olsen loved to travel, Kelly told the station.
"She never really stayed in one spot for too long," she said.