The Priory, in the city centre, is considering the move in response to a rise in enquiries.
Experts said a pilot scheme was about to start in Glasgow, and if it proved popular a similar scheme would be adopted in the Capital.
Last year, the clinic - known for its celebrity rehab work in London - had to switch to full-time hours to cope with demand from the Lothians.
Marco Bannerman, a hospital director for the company, said: "There is no doubt that work-related stress is a major problem in Scotland.
"Research shows that over half of Scottish workers have seen colleagues cry over pressure. By helping clients to identify the root causes of occupational stress, identifying unhelpful thinking styles and worrying management techniques, the workshops will instil confidence and coping skills."