The striker, who will join Juventus this summer, wishes circumstances had been different as his former boss is linked with a return to San Mames as he prepares to depart.
The striker endured a disappointing campaign at San Mames following his decision to sign a pre-contract agreement with Juventus in January, which will see him move to Turin when his contract expires on July 1.
Following being sacked by Valencia, Valverde has been strongly touted as a potential replacement for Marcelo Bielsa and a return to the club where he once played and coached, and Llorente admits he wishes he'd had the chance to work with him again.
"I have very fond memories of Ernesto," Llorente told Cadena SER's 'El Larguero' radio program. "I would have loved to continue with him, but circumstances have occurred otherwise, and I have another future apart from Athletic and hope to do well in Turin.
"I hope Valverde comes to Athletic Bilbao and takes them to the top. My debut with him was unforgettable and later [Joaquin] Capparos allowed me to grow, but my first season with Bielsa was my best with Athletic.
"In a few months I will go to Turin, and it will be more difficult for me to come back here. I feel nostalgic."
Los Leones finished 12th in La Liga, with Llorente finding the back of the net just four times in 26 league appearances.