Ten Cate's agent Sigi Lens said a deal for him to move to Chelsea as boss Avram Grant's assistant was in place.
Ten Cate said: "I know that Chelsea are interested in me.
"But not every story that does the rounds is true. I am coach at Ajax and my position is not up for discussion as far as I know."
He added: "Last year I came to Amsterdam because becoming champion with Ajax is my great dream.
"Despite the fact that we are now out of the Champions League and Uefa Cup I still feel secure in my position.
"I will be, as normal, on the bench when we meet Sparta Rotterdam on Sunday."