County have been searching for a new manager ever since they sacked Ian McParland earlier this month, despite him only losing four of his 14 matches in charge this term.
Big names such as former Inter boss Roberto Mancini have been linked with the job while former manager and current Crystal Palace chief Neil Warnock has also seen his name associated with the post.
However Eriksson has stressed that the club will choose the right man for the job and not just a big marquee name.
The news that Backe is being lined up may disappoint some County fans, with the 57-year-old unlikely to know the ins and outs of England's fourth tier.
Despite his low profile on these shores, Backe has won four Danish league titles with FC Copenhagen and Aalborg BK while he has also managed Panathinaikos in Greece.
Notts Co. 8/11, Draw 5/2, Shrewsbury 4/1