The 29 year old Spanish international had a solid debut season in the Serie A last term, and attracted the interest of Valencia earlier in the transfer window.
The Spanish outfit were rebuffed then, but are intent to sign a big name striker before the end of the window, and have re-entered the fray for the towering striker.
La Gazzetta Sportiva report that if a big enough offer does come from the cashed-up Valencia, then Juventus may be willing to sacrifice Llorente.
The money would then be used to try and convince Monaco to part ways with star striker Falcao.
Llorente scored 16 league goals in 33 appearances last season.