Joe van der Sar, 15, currently plays with VV Noordwijk at an amateur level and is regarded as an exciting prospect between the posts.
He has been involved in training sessions with Ajax and talks have now been held with Noordwijk regarding his future.
"Joe has a number of times trained at Ajax, and he has impressed many," Timo Gerlof, Noordwijk's Head of Technical Education, told West Broadcasting.
"We have not had contact with his parents, but Ajax have asked us to participate in this transition."
Edwin van der Sar spent nine years with Ajax at the start of his professional playing career, having also been with Noordwijk as a youngster.
He went on to play for Juventus and Fulham before finishing his career with a successful six-year stint at Manchester United, while he also made a record 130 appearances for the Netherlands at international level.