Convicted killer Anders Eklund is currently serving a life sentence for murdering two other people - 10-year-old Engla Höglund in 2008 and 31-year-old Pernilla Hellgren in 2000.
Police said they now had "reasonable grounds" to suspect him of killing a girl - known only as Jasmina - who disappeared 17 years ago in Sävsjö, southern Sweden.
Despite intense police efforts at the time, including around 800 interviews, the case is still unsolved.
Eklund was sentenced to life in prison in 2008 after the high-profile murder of Höglund.
The Swede ran across the 10-year-old as she was riding her bicycle home following football practice outside Stjärnsund in Dalarna in central Sweden.
Eklund followed the girl a short way and then began speaking to her, at which point, according to Eklund, she started acting “cheeky” and “arrogant”.
Afterwards, he said, he lost his senses and got “tunnel vision”.
He then raped and strangled the girl, and dumped her body in an isolated wooded area before trying to burn it.
Eight years earlier in June 2000, Eklund had followed Pernilla Hellgren, who was 31, as she left a street festival in Falun in central Sweden.
He later attacked, raped, and strangled her, leaving the body visible and partially clothed in a wooded area.