West Ham are also credited with interest in the Leeds centre-back, although Burnley are a new name on his list of admirers.
The Clarets twice raided Elland Road last summer, and a reunion with Charlie Taylor and Chris Wood across the Pennines - not to mention the prospect of European football next season, something West Ham cannot offer - could appeal to Jansson.
Burnley have made it through the campaign with only three recognised centre-backs in Ben Mee, James Tarkowski and Kevin Long.
And Jansson - who the report claims is also on the radar of clubs in Turkey and France - would be a welcome addition to Sean Dyche's side.
It is likely that Leeds will demand a substantial fee for the World Cup bound Swede, who signed a new five-year deal with them earlier this season.
Can Burnley see off West Ham to add another Leeds player?
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