Ten Cate, who was assistant to fellow Dutchman Frank Rijkaard at FC Barcelona before joining Ajax a year ago, reportedly met with Chelsea sporting director Frank Arnesen last week.
British papers reported Thursday that Ten Cate could join as early as next week, when the Premier League is on hiatus while players take part in international fixtures.
Grant took over when Jose Mourinho left two weeks ago, keeping Mourinho's assistant Steve Clarke in place, but the former Israel coach has said he wants to hire more help.
"Avram Grant has made it publicly clear several times that he intends to strengthen his back room team in addition to his assistant coach Steve Clarke," Chelsea said Thursday. "One of the scenarios Avram is considering is a team containing a British assistant coach in Steve and a foreign assistant coach, a system the first team are already familiar with."