Mata, a World Cup winner with Spain and a European champion with the country's Under-21 side earlier this summer, has been linked with moves to Liverpool, Tottenham, Manchester City and Arsenal, with the Gunners reportedly close to sealing a deal for the forward this week.
But Valencia claim they do not intend to sell and say the player is happy at Mestalla.
"I hope that he will stay with Valencia and I think he will do so. We have not received any offers for him so far," Vazquez told regional sports daily SuperDeporte.
"However, we have a back-up plan in case he leaves. That's not just the case for Juan, though. We have a plan like that for every player. We have to be prepared if something happens."
Vazquez claimed Mata was relaxed amid all the speculation.
"Juan is very calm and doesn't get carried away. Of course, the rumours don't go unnoticed, but there is absolutely no doubt about his commitment to Valencia," he said.