The 15 year-old prospect recieved an offer from Chelsea to leave Amsterdam for London.
But De Telegraaf says Ajax have convinced Van Axel Dongen and his family to stay with a contract offer to 2023.
The winger is set to now sign the deal.
The signing ceremony is expected to be held on September 29 - the day of Van Axel Dongen's 16th birthday.
Van Axel Dongen has been part of Ajax's youth academy since 2013. The Oranje youth international was previously with amateur clubs Zeeburgia and OSV.