Llorente has struggled for game time since his summer switch to Italy from Athletic Bilbao and reports have suggested he could be on the move already - although now he is featuring more frequently for the Turin-based that appears less likely.
Arsenal appear to have just found out to their cost according to Tuttosport, who claim the north London side have had a £20 million offer for the Spaniard turned down.
According to the publication, Juventus are confident that the 28-year-old, who found the back of the net in Juve's 2-2 draw with Real Madrid this week, is close to coming good and won't be convinced to let him leave in January or the summer.
TuttoSport add that Arsenal aren't the only ones who are interested in trying to land Llorente, with Barcelona and Real Madrid also said to be monitoring developments at the Juventus Stadium.
The Gunners are expected to be in the market for a new striker in the January transfer window in order to bring in back-up for Olivier Giroud - the club's only senior frontline forward.
Nicklas Bendtner is currently his deputy but has done little to suggest he is able to successfully deputise for the Frenchman were he to pick up an injury.