Chelsea are nearing an agreement for a deal worth €45 million (£38m/$49m) to sign the winger once the summer transfer window opens.
Goal can also confirm that the Blues attempted to sign Ziyech in January, but were informed by Ajax that a transfer at the end of the season was the preferred option.
Should the two clubs finalise a deal, Ziyech would become Frank Lampard's first signing since the former midfielder took over as manager of the Blues.
And Ten Hag all but confirmed that talks are progressing smoothly on Wednesday while also revealing that this is a move that has been expected for quite a while.
"Ziyech to Chelsea? A transfer was coming, we expected it to happen," the manager told Fox Sports. "And 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 scored 48 goals while providing 82 assists in 159 matches for Ajax since making the move to Amsterdam from FC Twente in 2016.
Following Ajax's run to the Champions League semi-finals last season, Ziyech was one of several stars expected to depart the club this past summer.
This season, Ziyech and Ajax sit atop the Eredivisie, with the Moroccan providing six goals and 12 assists in 18 league matches.
During the Champions League group stage, though, Ziyech was able to produce one stunning moment, scoring an incredible free-kick against what may just be his next club in the fixture at Stamford Bridge.