Quick, now called Sture Bergwall, was convicted of eight murders between 1994 and 2001 but has since withdrawn his confessions, and three of those convictions have now been quashed.
Justice Minister Ask says she wants to see the outcomes of the ongoing legal procedures to overthrow the remaining verdicts against Quick before she decides what form the review should take, news agency TT reports.
"I am concerned about this case", she told TT, "There are several questions that need to be answered. A person has been convicted of serious crimes, that we later find out they can't have been guilty of. That also means that we have several serious crimes where the perpetrators have gone free. And then we have the whole question as to how the justice system could have made these judgements."
Representatives from the opposition Social Democrats, Left and Green parties all say they would like some kind of commission to look into the police investigations and whether there was some kind of systematic fault in the legal system.