The Spanish international's agent, Jose Luis Tamargo, had earlier revealed Valencia's decision, which he said came after talks were held with three leading clubs he did not identify.
"We believe that Villa is the best striker in Europe and we have the good fortune to have him in Valencia so we are going to fight to keep him," Llorente said at a news conference.
"Today we took the decision to keep Villa and I cannot promise more than that," he added.
"There would have to be a scandalously scandalous offer and then we would think about it."
Villa, who is currently with the Spanish squad at the Confederations Cup in South Africa, has been strongly linked with Real Madrid and media have also reported interest from Barcelona and Chelsea with the player said to be in the 40 to 50 million euros price-range.
"They (Valencia) have put us through a situation that is, sadly, very unpleasant because this is no good for anyone," Tamargo said in a statement carried in the Spanish media.
Villa was the tournament top scorer at Euro 2008 with four goals, but missed Spain's 1-0 final victory over Germany due to injury. He has since become the nation's second-highest scorer with 30 goals, 14 behind leading marksman Raul on 44.
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