The Spaniard, a summer signing from Athletic Bilbao, has yet to score a goal for the Bianconeri and is currently behind Carlos Tevez and Mirko Vucinic in the striking pecking order
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Llorente is therefore touched that the club's fans are still showing him so much love from the stands.
"Many thanks to everyone for the trust shown in me and for continuing to believe in me," the forward wrote on his Facebook page.
"I want you to know that I am working day after day to repay your trust with great moments of happiness."
Llorente scored only four Liga goals during the final season of what was an otherwise successful spell at Athletic.