The 23-year-old has also been linked with a move to North London rivals Tottenham Hotspur and Italian side Inter Milan.
"Valencia simply rejected their offer," Mata's father told 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."
Mata has made 129 appearances for Los Che since joining in 2007 from Real Madrid.