Maurizio Sarri's side had offered a deal worth €65m (£58m/$73m) for De Ligt, €55m (£49m/$62m) up front with €10m in bonuses, although the Dutchman's omission from the tour squad would suggest talks have advanced further.
De Ligt's future has been the subject of much speculation over the summer, with a number of Europe's top clubs having been interested in signing him at one stage or another.
And the move appears to be close to completion after the Eredivisie side confirmed that De Ligt is not part of their 28-man squad travelling to Bramberg in Austria.
A short note from the club on the defender's absence read: "Awaiting a possible transfer, Matthijs de Ligt does not travel with the group."
De Ligt will not play a part in those games, however, with his final appearance for the club having seen him feature for the full 90 minutes in the 4-1 win over De Graafschap that sealed the Eredivisie title on May 15.
Sarri's side have already made six summer signings with Adrien Rabiot, Aaron Ramsey, Gianluigi Buffon, Luca Pellegrini and Merih Demiral all arriving, while Cristian Romero was purchased from Genoa before being loaned back.
Ajax have already taken steps to replace De Ligt by bringing in Heerenveen defender Kik Pierie and Lisandro Martinez, while Razvan Marin and Quincy Promes have also arrived in the summer.
And De Ligt's exit will be the second major departure from the club, with Frenkie de Jong having already joined Barca in a €75m (£67m/$84m) deal.