The Toffees are still searching for a new head coach following the sacking of Roberto Martinez, and it is believed they have the three-time Europa League-winning Spaniard on their short-list.
There have been suggestions that the 44-year-old could look to leave the Ramón Sánchez Pizjuán Stadium this summer, however, Castro insists Emery will not be leaving.
“The coach has understood our idiosyncrasies perfectly,” he told Sevilla TV.
“He is crazy about football, the hours he puts in, how he manages the squad. I say that now after being successful, but also at the start of the season.
“I can tell you he has said he is not on the market, and is not thinking about anything else.”