The details are outlined by a report in Marca, who say that the Andalusian club have no intention of negotiating for the goalkeeper, who has a €15m release clause in place in his current contract.
However, the offer from the Yellow Submarine stood at just €7m and was therefore not taken under serious consideration although the player is now into his final year of contract, so his future could be under scrutiny in the coming months.
The 26-year-old enjoyed a superb campaign for Granada last season and played an influential role in helping the club qualify for European competition for the first time ever.
Silva initially joined the club from Portuguese team Nacional in January 2017 and has now earned his first call-up to the Portuguese national squad, having previously been an Under-21 international.
Villarreal have already had a busy summer with the additions of Dani Parejo and Francis Coquelin from Valencia, alongside a loan deal for Real Madrid teenager Takefusa Kubo.