Asda's incoming chief operating officer Roger Burnley, who is not set to start his new job until October, is likely to be Clarke's successor.
Asda poached Burnley, a former Sainsbury’s top director, last year to become Clarke's right hand man.
In an interview with Retail Week Clarke said: "I said I wanted to find somebody who had the ability to be my successor.
“It took us some time to find the right person, the right cultural fit, the right sort of character and leader that can run the business."
Then news comes as the Walmart-owned supermarket posted a 5.7 per cent fall in like-for-like sales for the 13 weeks to 30 March.
Meanwhile, Walmart posted better-than-expected figures, with revenues reaching $115.9bn (£79.8bn). On a constant currency basis, total revenue was up four per cent to $119.4bn.