The 23-year-old, who has less than a year left on his current contract at Valencia, has long been linked with a move to the Gunners.
“Valencia simply rejected their offer,” said Mata’s father, Juan Manuel Mata Rodriguez, to calciomercato.com. “After some hesitation they answered ‘no’ to the Gunners’ offer.
“So my son remains a Valencia player, for now. But I don’t think it’s their last offer.
“There are several offers for Mata and I think that Arsenal will come forward again. The situation is still evolving.
“Are Inter Milan one of the interested teams? I know my son holds Milan in high esteem. We’ll see if Inter will come forward directly.”