The 23-year-old has been strongly linked to a move to the Emirates after the club reportedly tabled a bid for the winger last month.
Despite interest, Valencia have stood firm on the stance that their star player will remain in Spain.
"Mata has gone through a process of doubts about his future," said Emery. "But now we all believe he will stay at Valencia."
The Spaniard has kept quiet on where his future lies despite reports claiming that he was hoping for a move to the Gunners.
Mata was awarded the Bronze Boot for his two goals in the UEFA Under-21 Championship.