Mijailovic was sentenced to life imprisonment in 2004 for the murder of former foreign minister Anna Lindh.
Mijailo Mijailovic was born in Sweden to Serbian parents. He has previously expressed concerns for his own safety in Sweden and requested a move to Serbia.
Sweden has transferred prisoners to Serbia in the past but in each case a sentence has been decided in advance.
"When this has happened they have brought the cases to court first. Then we have been able to look at the verdict and the length of the sentence before reaching a decision," Richard Bernsten from the Swedish prison service told newspaper Dagens Nyheter.
Serious crimes can result in a maximum of 30 to 40 years in prison, according to the Serbian justice department.
"We will continue with our correspondence and we have not yet drawn any conclusions. But none of us here have any idea how this case is going to end," prison service spokeswoman Anne Marie Dahlgren told news agency TT.