Morrisons is said to be testing the concept known internally as Project Sarah at its Bradford head office. The store is open to its thousands of staff, with future plans to expand the idea more widely.
Then packing groceries as they go around, customers can leave without using a till and are automatically billed when they have finished shopping.
Customers will also be sent a receipt via email to keep track of their purchases.
There are now at least five Amazon Fresh stores in the UK with locations like White City and Ealing Broadway being extremely popular.
Tesco also recently announced plans to follow the tech giant, and tested its own store at its headquarters in Welwyn Garden City.
Perspex screens located at checkouts and in its cafes will also remain in place.
Meanwhile, Tesco is keeping its screens to help encourage social distancing.
UK CEO, Jason Tarry, outlined the latest rules and guidance in a message to Tesco shoppers.
Mr Tarry explained: “Throughout the pandemic, we’ve focused on making sure everyone can get the food they need in a safe environment.
“As Government guidance on COVID-19 continues to change, I wanted to share an update on the safety measures in our stores.
“While the easing of restrictions means that some safety measures will no longer be a legal requirement, we’ve listened to our customers and colleagues, and we know a lot of people remain cautious.
“In line with Government advice to act carefully, we feel it’s important to continue with certain measures to be on the safe side.”
This includes wearing face coverings while shopping in store.
Mr Tarry said: “Although the legal requirement to wear a face covering in England ends on July 19, the Government expects and recommends that people continue to wear a face covering in crowded and enclosed spaces.
“So we’re encouraging our colleagues and you, our customers, to continue wearing face coverings if you can.
“For our customers and colleagues in Scotland, Wales and Northern Ireland, face coverings remain mandatory unless exempt, as set out in Government guidance.”