Klaassen, 27, left Ajax for Everton in a €27m deal back in 2017, but endured a nightmare year in England.
Everton sold the 16-time Dutch international to Werder Bremen for €13.5m after one season, and he has impressed in Germany.
According to BILD, Ajax are prepared to offer between €8m and €9m to repatriate Klaassen.
However, Werder are likely to ask for a double-digit figure in excess of €10m for the midfielder.
Klaassen is under contract in Bremen until 2022 and has a market value of around €12m.
Werder barely avoided relegation to the 2. Bundesliga after edging out Heidenheim in a promotion/relegation playoff.
For Ajax, Werder’s survival is bad news as it makes their pursuit of former captain Klaassen more difficult.