The Portuguese shot-stopper comes off contract in June and is now free to commit to a pre-contract with any foreign club.
Currently, Rui Silva's deal carries a €15m buyout clause.
At Everton, manager Carlo Ancelotti counts on two senior goalkeepers - Jordan Pickford and Robin Olsen. Backup keeper Olsen is on-loan from AS Roma to June and Ancelotti has expressed an interest in signing the Swede permanently.
Rui Silva, 26, joined Granada three years ago from Portugal's Nacional and has been called into the senior national squad, though is yet to be capped. He has played for Portugal from U17-U21 level.
This season, Rui Silva has made 23 appearances for Granada, keeping nine clean sheets so far.
- updated December 5