Troubled retail giant Woolworths is set to be run by a foreigner after a search for a local executive to head the chain came up empty-handed.

In surprisingly frank comments, Woolworths chairman Gordon Cairns has admitted he invited several Australians to consider the job to replace Grant O'Brien but none were interested in even interviewing for the role.

"I couldn't persuade any of the local candidates I had in mind to come for an interview and I suspect the ones I had in mind were doing outstandingly well in their own organisations and the thought of working for me probably wasn't very attractive," Mr Cairns told The Australian Financial Review.