The 23-year-old was part of Spain's World Cup-winning squad in 2010 and was one of the stand-out players at this summer’s Under-21 European Championship.
The likes of Inter, Tottenham and the Gunners have been linked with a move for the midfielder this summer, and Juan Manuel Mata Rodriguez, the player's father, has now claimed that Arsene Wenger's side have had an initial offer rejected.
He told calciomercato.com: "Valencia simply rejected their offer. 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."
Goal.com exclusively revealed on Saturday that Mata would not be interested in a move to Arsenal's north London rivals Tottenham, although the player's father has admitted that Inter could be an option.
He added: "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."