The 6ft 5in Spain international joined the Bianconeri on a free transfer from Athletic Bilbao in the summer, but has struggled to hold down a regular first-team spot.
Llorente, who has been a reported January target of Arsenal, rescued a point in a dramatic 2-2 draw with Real Madrid in Tuesday's Champions League clash.
And despite only scoring one goal in eight appearances in the league this season, Llorente feels he is slowly adapting to life in Serie A.
"I've not been asked to leave," he told Radiogaceta de los Deportes. "What is being written in the papers is false. I have the complete faith of everyone at Juventus.
"It was not easy for me to adapt to the movement and play of the team, but I'm slowly managing to do what the boss wants.
"Once I have completely settled then everything will go well."