As reported by the Sun, David Wagner is looking to build on the Terriers' 16th place finish in the Premier League last season, and has identified Klasseen as a player who could add some extra quality to the squad.
Klaassen only signed for Everton prior to the beginning of last season for £23m, although the 25-year-old failed to settle at Goodison Park, making only 16 appearances in all competitions, seven of which came in the Premier League.
Wagner however does face competition in the shape of Bundesliga side Werder Bremen in the pursuit of Klaassen's signature, as they look to replace Thomas Delaney, who recently left the club to join Borussia Dortmund.
According to the report, the German side are willing to offer the Toffees £13m for the Netherlands international, which would a record figure for the club, although Everton are reluctant to make a £10m loss.
Despite struggling during his first season in English football, Klaassen was a key player for Ajax during his time in Holland.
Winning three Eredivisie titles and a Dutch Super Cup, the midfielder also appeared in the 2017 Europa League final for Ajax, although he finished on the losing side as Manchester United won 2-0.
Should new Everton manager Marco Silva deem Klaassen surplus to requirements, then it would free up funds to sign new players for the season ahead, as a deal for Watford's Richarlison worth an estimated £50m nears completion.