The Blues had an offer for the Holland international rejected by Ajax last week.
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News of Chelsea's bid sparked Arsenal into action, which have since made an approach to Ajax to also negotiate terms.
However, talkSPORT says Hato has now accepted a contract offer from Chelsea and is waiting on the two clubs to find agreement over a fee for his transfer.
The Blues tabled €40m for Hato, with Ajax making it clear he won't leave for less than €55-60m.