In December, Norwegian Justice Minister Anders Anundsen sent a proposal Ask about sending inmates from Norway to Swedish prisons.
The request comes as Norway struggles with a shortage of cells that police complain has forced them to release criminals back onto the streets.
While Sweden hasn't formally answered Anundsen's letter, Ask said there were a number of complicated legal aspects that prevented her from giving a green light to the proposal.
"What's problematic is that you probably have to change a number of laws to make that happen," she told the Svenska Dagbladet (SvD) newspaper.
Sending Norwegian inmates to Sweden would require that Sweden exercise authority in the name of Norway, or that Norwegian authorities get to permission operate in Sweden.
"And that's simply not the case, and that's what we're going to tell him," Ask said.
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She added, however, that she's open to exploring some sort of arrangement in the future where Norway and Sweden "could help one another".
Ask also acknowledged that Swedish prisons have spare capacity at the moment and that "we need to make sure we're not spending money unnecessarily on empty space".