Mata was part of the Spain squad which sealed a first World Cup triumph exactly a year ago and starred for their Under-21 side in their recent European Championship victory.
The Gunners and the Reds are thought to be interested in the 23-year-old, who would cost around 20million euros, but Valencia are adamant he will not be leaving the Mestalla.
"We have no intention of selling and we have not received any formal offers for the player," Llorente told Valencia-based sports daily Superdeporte.
"The news that has appeared in the papers is nothing more than speculation - Juan Mata is not for sale."
Lllorente says Valencia will be looking to strengthen their squad this summer, not weaken it.
"Our plan this summer is to make our squad better and our priority at the moment is to bring in a central defender," he said.
Valencia signed Almeria forward Pablo Piatti last week, but the Argentinian is seen as a replacement for Joaquin, who has joined Malaga.