The 23-year-old spent last season on loan at Wigan Athletic, before following Roberto Martinez to Goodison Park this summer.
However, the Spanish Under-21 international has failed to hold down a regular spot in the Toffees XI due to the form of long-serving goalkeeper Tim Howard.
According to AS, Sevilla are interested in signing the talented shot-stopper and will make their interest apparent when the transfer window opens.
Robles started his youth career at Getafe, before moving to Atletico Madrid in 2005. He departed the Calderon after making just two first-team league appearances.