Talks are under way for Alex Dyer to join the new Scotland head coach's backroom team while remaining as assistant manager at Killie.
The pair first worked together at West Ham, where Dyer was reserve coach and Clarke was Gianfranco Zola's number two. Dyer was later assistant manager of Charlton and Huddersfield.
Clarke stressed the appointment of a coaching staff would be his decision and he is in talks with other potential colleagues to fill a three- or four-man team.
"It's very important I have people who understand what makes me tick and how I want to put on training sessions and understand the message I want to put across to the players," he said.
"I am speaking to Kilmarnock and Alex Dyer to try and get Alex to come because he was a vital part of the recent success we had at Kilmarnock.
"Alex would come on a part-time basis and stay and help Kilmarnock, which is important to myself, Alex and Kilmarnock.
"And I have two or three other names in my mind I am speaking to and hopefully I can persuade one of those to come with me.
"If there's a possibility to bring someone else then I would look at that as well."