“I am manager of Southampton,” Koeman said. “Everyone knows I have one year more on my contract.
“We will sit together, analyse this season and talk about the future. That’s what the news is today.”
Valencia head coach Unai Emery, Stoke City manager Mark Hughes, Newcastle’s Rafael Benitez and Manchester City’s departing manager Manuel Pellegrini have all been linked with the Goodison Park vacancy.
De Boer – who recently left Ajax – has courted a move to England before with both Tottenham and Liverpool.
Koeman has achieved a 48% win percentage at Southampton, guiding them to eighth place in 2014-15, his first season in charge.
They could finish as high as fifth this term with if they win their final game of the season at home to Crystal Palace on Sunday and other results go their way.