Ceballos, 29, is expected to leave Real Madrid when the season concludes, with the club seeking around €15 million for a player entering the final year of his contract.
Fabrizio Romano has confirmed three clubs are in contact, with Ajax the most publicly identified.
The midfielder has made just 22 appearances this season for Real Madrid, accumulating 810 minutes — the third least among outfield players in the squad, behind David Alaba and Ferland Mendy, both of whom have suffered long-term injuries.
Under Álvaro Arbeloa he has made five appearances and has not featured at all in the last three games, including both Champions League quarter-final legs against Bayern Munich.
He came close to joining Marseille last August on a loan with an obligation to buy, with the two clubs reaching agreement, before Ceballos himself pulled out of the deal at the last moment — a decision that went down poorly with the club's hierarchy.
A return to Real Betis, his boyhood club where he began his professional career before moving to Madrid for €18 million in 2017, has been a recurring theme in speculation but Betis's financial constraints have repeatedly prevented a move.
Ajax are looking to add experienced players to complement their youth policy as they chase a first Eredivisie title since 2022. Two other unnamed clubs have also been in contact.