The suspect is a 25-year-old Senegalese man who had been spotted on CCTV alongside Ashley Olsen, an artist and event organiser who had lived in Florence for several years, the daily La Repubblica said.
The Corriere della Sera newspaper described him on its website as "a drug dealer... Who knew the victim."
Olsen's corpse was found at her flat in central Florence on Saturday afternoon. She had last been seen by friends at a nearby nightclub in the early hours of Friday.
The case has made the headlines in Italy, with the media suggesting it was the result of an erotic asphyxiation game which went wrong or she was strangled while in a semi-comatose state and unable to resist.
The case followed a lengthy legal saga surrounding another American expat in Italy, Amanda Knox, who was acquitted last year of involvement in the 2007 murder of her British flatmate Meredith Kercher.