Quick, who is now known as Sture Bergwall, has been cleared of eight murders which he confessed to committing to his therapist in 1994, while he was in psychiatric care. He was once described as Sweden's "worst serial killer of modern times".
Three of the eight victims were Norwegian and Norway had therefore expressed interest in participating in a review, Ask told Swedish Radio News.
"I have now contacted the Norwegian justice minister to see if Norway is prepared to and can contribute with their expertise," Ask said.
She added that the Norwegians have not responded yet but that several Norwegian politicians have expressed interest in the past.
In the autumn, the Swedish government will appoint a committee to review the way the eight murder cases were handled. In all cases, Bergwall was first convicted and then cleared. The committee will also investigate whether there are any structural shortcomings in the procedure for examining severe crimes in Sweden.
Ask also mentioned the possibility of finding foreign experts who can provide a fresh perspective since many top Swedish lawyers have been involved in the Thomas Quick case at some point over the past two decades.
She told Swedish Radio News: "I think it is very important... Sweden is a small country and the question is: are there structural problems which could lead to these types of scandals happening again in the future and in what way can we correct that?"
"I am convinced that you have to look at this matter from several different perspectives," Ask added.
Bergwall, 63, was convicted of the string of murders between 1994 and 2001, largely on the strength of his confessions and without forensic evidence. He withdrew his confessions in 2008. In July, prosecutors dropped the charges in the last of eight murder convictions against him.