Phelps has held the top drinks post for the last three years, having worked his way up ranks since joining the company as a graduate trainee.
He has worked in a number of buying positions including meat and frozen food. Phelps is rumoured to be in discussions with the Co-operative Group.
Both Sainsbury’s and the Co-op declined to comment.
Rumours of Phelps’ departure come as Sainsbury’s announced today it would cut 800 jobs as it restructures amid tough trading conditions.
The redundancies are part of a plan reported last November to save £500m over the next three years.