Mata has been linked with a move to the Emirates since starring in the European Under-21 Championships, but talk of a Premier League switch was quashed by his current club 10 days ago when president Manuel Llorente explicitly claimed, "Juan Mata is not for sale".
However, the La Liga club, who cashed in on David Villa and David Silva last summer, now appear willing to back-flip on that stance should the right offer come for Mata.
"The possibility exists that Mata will leave the club," Valencia manager Unai Emery told Marca.
"We want him to stay and Mata has also expressed his desire to stay at Valencia, but at the same time we cannot stop a player who really wants to leave for money or for a bigger club. So, if there is a large financial offer from any club, that is good for both us and him, we will have to let him leave."
Tottenham and Liverpool are also believed to be interested in the winger, but Arsenal's potential to offer Champions League football next season is understood to put the Gunners as frontrunners for Mata's signature.