The municipalities that have reported their interest are Emmaboda, Kristianstad, Hässleholm, Karlskrona, Hörby, Forshaga, Klippan, Eskilstuna, Osby, Sundsvall, Vilhelmina, Ånge and Luleå.
The new facility is estimated to provide 250 new jobs.
-Of course, this is important to us. It's about hundreds of jobs. The institute would become one of the largest employers alongside the municipality itself, Hans Bertil Sinclair (M), municipal council in Klippan, told the radio.
The referendum in Svedala was carried out after collecting 2,300 signatures by opponents to the prison. More than 7,000 voted no and just under 3,000 people voted yes. Among the opponents, there were many who considered that a house would make Svedala unsafe.