The Nordsjaelland star, who can play both as a midfielder and an attacker, will reportedly put pen to paper on a five-year deal in the coming days.
Dutch media outlet FootballOranje reports that Ajax will fork out €9 million to price the 19-year-old away from the Danish outfit.
Should the move be confirmed, Kudus will become the most expensive teenager in the history of Ghana football.
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The former Right to Dream academy star will turn 20 on August 2, so the move will need to be official before then for him to go into the history books.
This is because other Ghanaian youngsters have commanded bigger transfer fees than the €9 million Ajax is offering for Kudus, but most of them were past their teenage years.
In 2015, Atletico Madrid paid €10 million to price Bernard Mensah away from Vitoria Guimaraes. The midfielder was 20 years when the joined the Rojiblancos.
Also, Abdul Baba Rahman was just 21 when he completed a £21.7million move from Augsburg to Chelsea.
Kudus joined Nordsjaelland in 2018 and has since developed into one of the most important players at the club.
The 19-year-old has netted 12 times in 26 appearances for the Danish Superliga side this season.