Quoting reports from Italian newspaper Gazzetta dello Sport, the report claims Juventus are confident of beating Arsenal and Liverpool to Llorente - and for just £5m.
The Spain international is out of contract in Bilbao at the end of the season, and has been linked with a move to Serie 'A' and the Premier League.
Arsenal and Liverpool were thought to be the most likely destinations in England - both clubs need a first-class striker - but Juventus have also been linked with a number of Europe's best strikers.
And it seems the Italian champions have honed in on Llorente, as Juventus's forwards have managed just 12 goals between them so far this term.
The Italian giants were reported to be interested in Robin Van Persie and Luiz Suarez last summer, but eventually only signed Nicklas Bendtner from Arsenal on loan.
And they prolificacy in front of goal has already cost them this season, as Inter Milan ended their 49-match unbeaten run last weekend.
Gazzetta dello Sport claims Juventus are already in advanced talks with the player's agent regarding a possible deal for Llorente, all but ending Arsenal and Liverpool's hopes of signing the Spain striker in January.