Sky Sports News reported earlier on Tuesday that a deal was close for the Spain international as the Premier League new boys look to strengthen their defence.
"Eskerrik asko, thank you! We wish you the best of luck in this new stage of your career, Diego!"
Llorente started his career at Real Madrid and joined Sociedad in 2017 after loan spells at Rayo Vallecano and Malaga.
The 27-year-old made his debut for Spain in 2016 and has featured five times for his country.