The Toffees, who avoided relegation on the final day of the Premier League season, are ready to strengthen their squad.
Per Phillipp Hinze, German sides Mainz and Borussia Monchengladbach are also interested in Krauss.
However, Everton are the financially strongest of the candidates, giving them an edge.
The Toffees would be prepared to pay the €7 million that Schalke are seeking.
The Leipzig-born 21-year-old enjoyed an outstanding season this term.