The Italian club have already secured the services of promising youngsters such as M’Baye Niang and Gabriel in the summer transfer window, and they have earmarked 19-year-old Klaassen as their next youthful, potential addition.
Klaassen is a product of the Ajax youth academy, and has been compared to Dennis Bergkamp for his intelligent positioning and movement.
The attacking midfielder, who can also play as a forward, made his official first team debut in the Champions League match against Lyon last season, and has so far netted once in 10 appearances for the Eredivisie champions.
However, Klaassen will not be available on the cheap if Milan decide to step up their chase for the Netherlands Under-21 international. He has a contract with Ajax until the summer of 2016, and the Amsterdam giants value the hot prospect at €7 million.