Ziyech came off the bench during Wednesday’s 3-0 KNVB Beker victory at Vitesse and Ten Hag provided an update on the 26-year-old Morocco international.
“Ziyech to Chelsea? A transfer was coming, we expected it to happen,” Ten Hag told Fox Sports post-game.
“I actually already expected this one or two years earlier. And each time it was: ‘Wow, he stayed again’.
“We are just happy that we will still have him until the end of the season.”
Ziyech has been directly involved in 166 goals since his Eredivisie debut in 2012-13, contributing 79 goals and 87 assists.
Since joining Ajax from Twente in 2016, Ziyech has scored 38 league goals and 48 across all competitions.
Ziyech’s sensational tally of 51 Eredivisie assists from the beginning of the 2016-17 campaign is 16 better than the 35 of Steven Berghuis, the next highest during that period, while his 421 chances created since September 2016 is a whopping 134 more than his nearest rival.
Ten Hag added: “I am not surprised by the news about Ziyech. I know that our players are very popular with the big clubs in Europe. That is just great.
“I have known for a long time what Hakim wants. He has a picture in mind. He knows exactly which clubs he finds interesting and which ones are not.
“Chelsea are a fantastic club. When it is final, I am very happy for Hakim, and I am very proud of him.”