Dalton Park, which in recent years has added a cinema, a pub and several restaurants, is currently shut due to restrictions in place to limit the spread of COVID-19.
Morrisons has been contacted for further comment.
Comments on the proposals can be submitted to Durham County Council until Monday, June 8.
A message from the Editor:
Thank you for reading this story on our website. While I have your attention, I also have an important request to make of you.
In order for us to continue to provide high quality and trusted local news on this free-to-read site, I am asking you to also please purchase a copy of our newspaper.
Our journalists are highly trained and our content is independently regulated by IPSO to some of the most rigorous standards in the world. But being your eyes and ears comes at a price. So we need your support more than ever to buy our newspapers during this crisis.
With the coronavirus lockdown having a major impact on many of our local valued advertisers - and consequently the advertising that we receive - we are more reliant than ever on you helping us to provide you with news and information by buying a copy of our newspaper.