In January, the 26-year-old confessed to stabbing Lindh Sept. 11, 2003, outside a Stockholm department store, and was convicted of the murder by a district court. That was overturned on appeal, and he was sentenced to psychiatric detention.
Mijailovic was also ordered to pay about $15,000 in damages to the family of Lindh, who was 46 when she was killed.
CNN said Mijailovic's lawyer, Mikael Nilsson was seeking to have his client transferred to serve his sentence in Serbia-Montenegro, his parents' homeland.
"He will try to be transferred away from Sweden and serve his sentence there," he told Swedish radio.
Mijailovic confessed to police in January, saying inner voices speaking in Serbian told him to attack, and he believed it was the voice of Jesus.