The bid reportedly fell short of the €20 million (£17m) release clause in Mosquera's contract, which is set to expire at the end of next season.
Valencia seems unwilling to negotiate a lower fee for Mosquera despite his contract situation. This could lead to a stalemate between the two clubs.
However, there are suggestions that personal terms between Arsenal and Mosquera have already been agreed upon, which could influence their decision-making process.
Arsenal will likely try to find a resolution soon, as they face competition from other top clubs, including Chelsea and Manchester City, who have previously shown interest in Mosquera.